Design Of 10m Clear Span Slab Bridge l3x4t

Construction of 10.00mts span culvert at 5/6 KM of Vemuladeevi channel Name of the work:-Construction of bridge across Dharbharevu canal on Gopuram road near Anjaneyaswamy temple in Pedalanka(V)

n of 10.00mts span culvert at 5/6 KM of Vemuladeevi channel

he work:-Construction of bridge across Dharbharevu canal uram road near Anjaneyaswamy temple in Pedalanka(V)

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: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 and area by considering actual cross-section of the channel. Step2: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. The vertical clearence and afflux are verified. 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 below the maximum scour depth Step3:After arriving at bottom of deck level,bottom of foundation level and required ventway,the dimensions of the bridge are finalised. The structural components are desined in the following manner:a.As per the recommendations of IRC 6:2000,IRC class A live load required for bridges and culverts of medium importance is selected. 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 designed as per the guide lines given in relevent IRC codes. 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

Deck slab length

=

10.740m

Width of the carriage way

=

5.50m

Thickness of deck slab as per MOST Dg.BD 3-74

=

0.790m

Thickness of wearing coat

=

0.075m

Height of railing

=

1.200m

Thickness of dirt wall

=

0.30m

Sectional area of dirt wall

=

0.440sqm

Thickness of RAFT footing

=

0.70m

Height of abutments

=

1.664m

Top width of abutments

=

0.690m

Bottom width of abutments

=

2.00m

Sectional area of abutment section

=

2.238sqm

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

Canal side offset of 1st footing wrt abutment

=

0.15m

Bank side offset of 1st footing wrt abutment

=

0.15m

Width of 2nd footing

=

2.45m

Thickness of 2nd footing

=

0.30m

Canal side offset of 2nd footing wrt abutment

=

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

Thickness of VRCC RAFT footing

=

0.60m

Type of bearings

=

Unit weight of RCC (yrc)

=

25KN/cum

Unit weight of PCC (ypc)

=

24KN/cum

Density of back fill soil behind abutments (y)

=

18KN/Cum

Unit weight of water (yw)

=

10KN/Cum

(As per hydralic calculations)

No bearings proposed

Angle of shearing resistance of back fill material(Q)

=

30

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

=

51.81

Slope of back fill (b)

=

0

Angle of wall friction (q)

=

15

Height of surcharge considered (h3)

=

1.20m

Road crest level (RTL)

=

2.862m

Low bed level (LBL)

=

0.488m

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

= = =

1.488m -1.512m 6.00t/sqm

Compressive strength of concrete for RCC Strip footing (fck)

=

25.00N/sqmm

Yield strength of steel (fy)

=

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 slab culvert:1.Dead load 2.Live load 3.Impact load 4.Wind load 5.Water current 6.Tractive,braking effort of vehicles&frictional resistance of bearings 7.Buoyancy 8.Earth pressure 9.Seismic force 10.Water pressure force

As per clause 202.3,the increase in permissible stresses is not permissible for the above 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

Self wieght of the abutments upto bottom most footing based on the preliminary section assumed:iv)Self wieght of the abutment section =

295.42KN

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

483.52KN

W1

W1

ix)Calculation of eccentricity of self weight of abutment w.r.t base of abutment S.No

Description Load in KN

Distance of centroid of load from toe of abutment

Moment

1

Back batter(W1)

143.86944

1.127

162.14

2

Centre portion(W2)

151.55712

0.345

52.29

3

Front batter(W3)

0

0

0

295.42656 Location of resultant from toe of abutment =

214.43 0.73m

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 S.No


Distance of centroid of load from toe of 1st footing

Moment

1

Back batter

143.86944

1.277

183.72

2

Centre portion

151.55712

0.495

75.02

3

Front batter

0

0

0

4

1st footing

91.08KN

1.15

104.74

386.50656

363.48

Location of resultant from toe of abutment =

0.94m

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

S.No


Moment

Distance of centroid of load from toe of 2nd footing

1

Back batter

143.86944

1.427

205.3

2

Centre portion

151.55712

0.645

97.75

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

483.52656

540.3


1.12m

Eccentricity =

0.105m

xii)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 2nd footing S.No

1 2 3 4 5 6


Back batter Centre portion Front batter 1st footing 2nd footing 3rd footing

Moment

Distance of centroid of load from toe of 3rd footing

0 0 0 0 0 0 0

1.427 0.645 0.3 1.00 0.93 0.00

0 0 0 0 0 0 0


0.00m

Eccentricity =

0.000m

2.Live Load:As per clause 201.1 of IRC:6--2000,the bridges and culverts of medium importance are to be designed for IRC Class A loading. GENERAL IRC Class-A loading Pattern

1.10

3.20

1.20

4.30

3.00

3.00

3.00

1.80 3.00

6.8t

3.00

6.8t

4.30

6.8t

1.20

6.8t

3.20

11.4t

11.4t

2.7t

2.7t

1.10 3.00

The IRC Class A loading as per the drawing is severe and the same is to be considered as per clauses 207.1.3&207.4

Y 475

11.4t

11.4t

Portion to be loaded with 5KN/m² live load 6.8t

10000

11380

6.8t

X

5500 2925

3525

The ground area of wheels for the above placement,each axle wise is given below:Axle load (Tonnes) 11.4 6.8

Ground Area B(mm)

250 200

W(mm)

500 380

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

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

0.625m

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

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

Wheel Load/UDL in KN

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

586.855

1543.90KNm

Distance of centroid of forces from y-axis

= 2.631m Eccentricity =

0.594m

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 Eccentricity =

Y

2.441m

Location of Resultant

2631

10000

11380

2631

10000

11380

7131

X

5500

Calculation of reactions on abutments:-

Reaction due to loads Ra =

367.74KN

Reaction due to point loads = Rb =

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 area on the abutment,

300 185

300

815 815

815 815 740

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

0.269

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)

2.37m

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 Kg/m2. Height of the deck system =

2.065

Breadth of the deck system =

11.38

The effective area exposed to wind force =HeightxBreadth = Hence,the wind force acting at centroid of the deck system = (Taking 50% perforations)

6.97KN

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 =

The location of the wind force from the top of RCC raft footing =

16.50KN

4.93m

5.Water current force:Water pressure considered on square ended abutments as per clause 213.2 of IRC:6---2000 is P = 52KV2 =

26.286 Kg/m2.

(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 =

0.62KN

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

3.77m

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 s of simply ed 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 =

7.Buoyancy :-

4.63m

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 =

12.31Cum

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 20.15Cum

Reduction in self wieght =

201.47KN

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 '2 Ka =

Sin(a+Q) sina

sin(a-q)

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

Sin(a+Q) = Sin(a-q) = Sina = Sin(Q+q) = Sin(Q-b) = Sin(a+b) =

SIN[3.14*(51.81+30)/180] = SIN[3.14*(51.81-15)/180] = SIN[3.14*(51.81)/180] = SIN[3.14*(30+15)/180] = SIN[3.14*(30-0)/180] = SIN[3.14*(51.81+0)/180] =

0.99 0.599 0.786 0.707 0.5 0.786

From the above expression, Ka =

0.76

The hieght of abutment above GL,as per the preliminary section assumed = Hence,maximum pressure at the base of the wall

1.664m Pa =

22.76KN/sqm

The pressure distribution along the height of the wall is as given below:Surcharge load =

16.42 KN/sqm

16.42

1.664

22.76

16.42

Area of the rectangular portion = Area of the triangular portion =

27.32 18.94 46.26

Taking moments of the areas about the toe of the wall S.No 1 2

Description

Area

Lever arm Moment

Rectangular Triangular

27.32 18.94

0.832 22.73024 0.55466667 10.50538667

46.26

33.23562667

Height from the bottom of the wall =

0.72m

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

0.70

53.19 1.664m 0.72m 51.81

2.00 0.57 Total earth pressure acting on the abutment P =

254.43KN

Horizontal component of the earth pressure Ph =

152.54KN

Vertical component of the earth pressure Pv =

203.63KN

Eccentricity of vertical component of earth pressure = 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 1.488m

3.00

BFL -1.512m

0.43m

30.00kn/sqm

Total horizontal water pressure force =

247.50KN

The above pressure acts at height of H/3 =

1.00m

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 Vertical forces acting on the abutment (P) composes of the following components S.No

Type of load

Intensity in KN

Eccentricty about x- Eccentricty about yaxis(m) axis(m)

1

Reaction due to dead load from super structure

699.20KN

-0.740

0.00

2

Self wieght of abutment&footings

483.53KN

0.105

0.000

3

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

-0.740

0.000

4

Impact load

0.00

0.00

466.66KN 0.00 1649.38

Horizontal forces acting/transferred on the abutment (H) composes of the following components S.No

Type of load

Intensity in KN

Direction x or y

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

1

Wind load

16.50KN

x-Direction

4.93

2

Tractive,Braking&Frictional resistance of bearings

58.69KN

y-Direction

4.63

3

Water current force

0.62KN

x-Direction

3.77

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 = Section modulus of bottom footing about x-axis --Zx =

15.3125 m2 (1/6)bd2 =

6.25 m3

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

i.e, 5000KN/sqm For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2 i.e, -2800KN/sqm S.No

1 2 3 4 5

Type of load

Intensity in KN (P)

Vertical loads:-(Stress = P/A(1+6e/b) Reaction due to dead load from super structure Self wieght of abutment&footings Reaction due to live load with impact factor Impact load Horizontal loads:- (Stress = M/Z) Tractive,Braking&Frictional resistance of bearings

Eccentricity/Lever arm

Stress at heel P/A(1+6e/b)

699.20KN 483.53KN 466.66KN 0.00KN

-0.740 0.105 -0.740 0.000

13.22 34.76 8.83 0

58.69KN

4.63

-43.46 13.35

S.No

1 2 3 4 5

Type of load

Eccentricity

Intensity in KN (P)


Stress at toe P/A(1+6e/b)

699.20KN 483.53KN 466.66KN 0.00KN

0.740 -0.105 0.740 0.000

78.1 28.39 52.13 0

58.69KN

4.63

43.46 202.08

Stress at heel =

P/A(1+6e/b)+M/Z =

13.35 KN/Sqm>-2800KN/sqm.

Hence safe. Stress at toe =

P/A(1+6e/b)+M/Z =

202.08 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 = Section modulus of bottom footing about = y-axis--Zy =

15.3125 m2 (1/6)bd2 =

15.95 m3

For M20 grade of concrete permissible compressive stress in direct compreession is 4N/mm2 i.e, 5000KN/sqm For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2 i.e, -2800KN/sqm

S.No

1 2 3 4 5 6

Type of load

Intensity in KN (P)

Vertical loads:-(Stress = P/A(1+6e/b) Reaction due to dead load from super structure Self wieght of abutment&footings Reaction due to live load with impact factor Impact load Horizontal loads:- (Stress = M/Z) Wind load Water current force


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

699.20KN 483.53KN 466.66KN 0.00KN

0.00 0.00 0.000 0.00

45.66 31.58 30.48 0

16.50KN 0.62KN

4.93 3.77

-5.1 -0.15 102.47

S.No

1 2 3 4 5 6

Type of load

Intensity in KN (P)


Stress at up stream side edge =

P/A(1+6e/b)+M/Z =


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

699.20KN 483.53KN 466.66KN 0.00KN

0.00 0.00 0.000 0.00

45.66 31.58 30.48 0

16.50KN 0.62KN

4.93 3.77

5.1 0.15 112.97

102.47 KN/Sqm>-2800KN/sqm.

Hence safe. Stress at down stream side edge =

P/A(1+6e/b)+M/Z =


Hence safe.

i)On top of 2nd footing 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 Vertical load acting on the abutment (P) composes of the following components S.No

Type of load

Intensity in KN


1


699.20KN

-0.740

0.00

2

Self wieght of abutment&cut waters

386.51KN

0.210

0.000

3

Reaction due to live load with impact factor

-0.740

0.000

4

Impact load

0.000

0.00

466.66KN 0.00

Horizontal load acting/transferred on the abutment (H) composes of the following components S.No

Type of load

Intensity in KN

Direction x or y


1

Wind load

16.50KN

x-Direction

4.63

2


58.69KN

y-Direction

4.33

3

Water current force

0.62KN

x-Direction

3.47

Check for stresses:About x-axis:Breadth of 1st footing b = Depth of 1st footing d = Area of the footing = A = Section modulus of base of abutment about x-axis--Zx =

6.25m 2.30m 14.375 m2 (1/6)bd2 =

5.51 m3

For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2 i.e, 5000KN/sqm For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2 i.e, -2800KN/sqm S.No

1 2 3 4 5

Type of load


Intensity in KN (P)



699.20KN 386.51KN 466.66KN 0.00KN

-0.74 0.21 -0.74 0.00

14.09 29.24 9.4 0

58.69KN

4.33

-46.11 6.62

S.No

1 2 3 4 5

Type of load


Intensity in KN (P)

Eccentricity


699.20KN 386.51KN 466.66KN 0.00KN

0.74 -0.21 0.74 0.00

83.19 21.47 55.53 0

58.69KN

4.33

46.11 206.3

Stress at heel =

P/A(1+6e/b)+M/Z =



P/A(1+6e/b)+M/Z =


Hence safe. About y-axis:Breadth of 1st footing b = Depth of 1st footing d = Area of the footing = A =

2.30m 6.25m 14.375 m2

Section modulus of base of abutment about y-axis--Zy =

(1/6)bd2 =

14.97 m3


i.e, 5000KN/sqm For M20 grade of concrete permissible tensile stress in bending tension is -2N/mm 2 i.e, -2800KN/sqm S.No

1 2 3 4 5 6

Type of load


Intensity in KN (P)



699.20KN 386.51KN 466.66KN 0.00KN

0.00 0.00 0.000 0.00

48.64 26.89 32.46 0

16.50KN 0.62KN

4.63 3.47

-5.1 -0.14 102.75

S.No

1 2 3 4 5 6

Type of load


Stress at up stream side edge of abutment =

P/A(1+6e/b)+M/Z =

Intensity in KN (P)



699.20KN 386.51KN 466.66KN 0.00KN

0.00 0.00 0.000 0.00

48.64 26.89 32.46 0

16.50KN 0.62KN

4.63 3.47

5.1 0.14 113.23

102.75 KN/Sqm>-2800KN/sqm.

Hence safe. Stress at down stream side edge of abutment =

P/A(1+6e/b)+M/Z =


Hence safe. i)On top of 1st footing 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 Vertical load acting on the abutment (P) composes of the following components S.No

Type of load

Intensity in KN

1 2 3

Reaction due to dead load from super structure Self wieght of abutment&footings Reaction due to live load with impact factor

4

Impact load


699.20KN 295.43KN 466.66KN 0.00

-0.815 0.270 -0.815

0.00 0.000 0.000

0.000

0.00


1 2 3

Type of load

Intensity in KN

Wind load Tractive,Braking&Frictional resistance of bearings Water current force

Direction x or y

16.50KN 58.69KN 0.62KN

x-Direction y-Direction x-Direction

Location(Ht.from the section considered). (m) 4.33 4.03 3.17

Check for stresses:About x-axis:Breadth of abutment b = Depth of abutment d = Area of the footing = A = Section modulus of base of abutment about x-axis--Zx =

6.25m 2.00m 12.5 m2 (1/6)bd2 =

4.17 m3


Type of load

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

Intensity in KN (P)



1 2 3 4 5

Reaction due to dead load from super structure Self wieght of abutment&footings Reaction due to live load with impact factor Impact load Horizontal loads:- (Stress = M/Z) Tractive,Braking&Frictional resistance of bearings

699.20KN 295.43KN 466.66KN 0.00KN

-0.82 0.27 -0.82 0.00

12.17 26.7 8.12 0

58.69KN

4.03

-56.76 -9.77

S.No

1 2 3 4 5

Type of load

Intensity in KN (P)


Eccentricity


699.20KN 295.43KN 466.66KN 0.00KN

0.82 -0.27 0.82 0.00

99.7 17.51 66.54 0

58.69KN

4.03

56.76 240.51

Stress at heel =

P/A(1+6e/b)+M/Z =

-9.77 KN/Sqm>-2800KN/sqm.


P/A(1+6e/b)+M/Z =


Hence safe. About y-axis:Breadth of abutment b = Depth of abutment d = Area of the footing = A = Section modulus of base of abutment about y-axis--Zy =

2.00m 6.25m 12.5 m2 (1/6)bd2 =

13.02 m3


i.e, 5000KN/sqm For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2 i.e, -2800KN/sqm S.No

1 2 3

Type of load

Vertical loads:-(Stress = P/A(1+6e/b) Reaction due to dead load from super structure Self wieght of abutment&footings Reaction due to live load with impact factor

Intensity in KN (P)

699.20KN 295.43KN 466.66KN


0.00 0.00 0.000


55.94 23.63 37.33

4 5 6

Impact load Horizontal loads:- (Stress = M/Z) Wind load Water current force

0.00KN

0.00

0

16.50KN 0.62KN

4.33 3.17

-5.49 -0.15 111.26

S.No

1 2 3 4 5 6

Type of load

Intensity in KN (P)



P/A(1+6e/b)+M/Z =



699.20KN 295.43KN 466.66KN 0.00KN

0.00 0.00 0.000 0.00

55.94 23.63 37.33 0

16.50KN 0.62KN

4.33 3.17

5.49 0.15 122.54

111.26 KN/Sqm>-2800KN/sqm.


P/A(1+6e/b)+M/Z =


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 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 Vertical load acting on the abutment (P) composes of the following components S.No

1

Type of load

Intensity in KN


699.20KN


483.53KN

Reduction in self weight due to buoyancy

-201.47KN

2

Net self weight

3

Vertical component of earth pressure

Eccentricty about x- Eccentricty about yaxis(m) axis(m) -0.740

0.00

282.06KN

0.105

0.000

203.63KN

0.430

0.000

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

S.No

Type of load

Intensity in KN

Direction x or y


1

Wind load

16.50KN

x-Direction

4.93

2


0.00KN

y-Direction

0.00

3

Water current force

0.62KN

x-Direction

3.77

4

Horizontal load due to earth pressure

152.54KN

y-Direction

1.32

5

Water pressure force

247.50KN

y-Direction

1.00

Check for stresses:About x-axis:Breadth of bottom footing b = Depth of bottom footing d = Area of the footing = A =

6.25m 2.45m 15.3125 m2

Section modulus of bottom footing about x-axis --Zx =

(1/6)bd2 =

6.25 m3


1 2 3 4 5

Type of load

Vertical loads:-(Stress = P/A(1+6e/b) Reaction due to dead load from super structure Net self wieght of abutment&footings Vertical component of Earth pressure Horizontal loads:- (Stress = M/Z) Horizontal load due to earth pressure Water pressure force

S.No

1 2 3 4 5

Type of load


Stress at heel =

P/A(1+6e/b)+M/Z =

Intensity in KN (P)



699.20KN 282.06KN 203.63KN

-0.74 0.11 0.43

13.22 20.28 18.79

152.54KN 247.50KN

1.32 1.00

-32.17 39.6 59.7

Intensity in KN (P)

Eccentricity


699.20KN 282.06KN 203.63KN

0.74 -0.11 -0.43

78.1 16.56 7.81

152.54KN 247.50KN

1.32 1.00

32.17 -39.6 95.06



P/A(1+6e/b)+M/Z =


Hence safe.

About y-axis:Breadth of bottom footing b = Depth of bottom footing d = Area of the footing = A =

2.45m 6.25m 15.3125 m2

Section modulus of bottom footing about y-axis --Zy =

(1/6)bd2 =

15.95 m3


1 2 3 4 5

S.No

1 2 3 4 5

Type of load

Intensity in KN (P)

Vertical loads:-(Stress = P/A(1+6e/b) Reaction due to dead load from super structure Net self wieght of abutment&footings Vertical component of Earth pressure Horizontal loads:- (Stress = M/Z) Wind load Water current force

Type of load


P/A(1+6e/b)+M/Z =

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

699.20KN 282.06KN 203.63KN

0.00 0.00 0.00

45.66 18.42 13.3

16.50KN 0.62KN

4.93 3.77

-5.1 -0.2 72.13

Intensity in KN (P)



Eccentricity


699.20KN 282.06KN 203.63KN

0.00 0.00 0.00

45.66 18.42 13.3

16.50KN 0.62KN

4.93 3.77

5.1 0.2 82.63



P/A(1+6e/b)+M/Z =

Hence safe.


ii)On top of 2nd footing 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 Vertical load acting on the abutment (P) composes of the following components S.No

1

Type of load

Intensity in KN



699.20KN

-0.74

0.00

Self wieght of abutment&footings

483.53KN


-201.47KN

2

Net self weight

282.06KN

0.105

0.000

3


203.63KN

0.430

0.000


Type of load

Intensity in KN

Direction x or y


1

Wind load

16.50KN

x-Direction

4.63

2


0.00KN

y-Direction

0.00

3

Water current force

0.62KN

x-Direction

3.47

4


152.54KN

y-Direction

1.02

5


247.50KN

y-Direction

0.70

Check for stresses:About x-axis:Breadth of 2nd footing b = Depth of 2nd footing d = Area of the footing = A = Section modulus of bottom footing about x-axis --Zx =

6.25m 2.30m 14.375 m2 (1/6)bd2 =

5.51 m3


Type of load

Intensity in KN (P)



1 2 3 4 5


S.No

1 2 3 4 5

Type of load

-0.74 0.11 0.43

14.09 21.6 20.01

152.54KN 247.50KN

1.02 0.70

-28.19 31.4 58.95

Intensity in KN (P)


Stress at heel =

699.20KN 282.06KN 203.63KN

P/A(1+6e/b)+M/Z =

Eccentricity


699.20KN 282.06KN 203.63KN

0.74 -0.11 -0.43

83.19 17.64 8.32

152.54KN 247.50KN

1.02 0.70

28.19 -31.4 105.9



P/A(1+6e/b)+M/Z =


Hence safe.

About y-axis:Breadth of 1st footing b = Depth of 1st footing d = Area of the footing = A = Section modulus of bottom footing about y-axis --Zy =

2.30m 6.25m 14.375 m2 (1/6)bd2 =

14.97 m3


1 2 3 4

Type of load

Vertical loads:-(Stress = P/A(1+6e/b) Reaction due to dead load from super structure Net self wieght of abutment&footings Vertical component of Earth pressure Horizontal loads:- (Stress = M/Z) Wind load

Intensity in KN (P)



699.20KN 282.06KN 203.63KN

0.00 0.00 0.00

48.64 19.62 14.17

16.50KN

4.63

-5.1

5

Water current force

S.No

1 2 3 4 5

0.62KN

Type of load

Intensity in KN (P)



P/A(1+6e/b)+M/Z =

3.47

Eccentricity

-0.1 77.19


699.20KN 282.06KN 203.63KN

0.00 0.00 0.00

48.64 19.62 14.17

16.50KN 0.62KN

4.63 3.47

5.1 0.1 87.67



P/A(1+6e/b)+M/Z =


Hence safe.

iii)On top of 1st footing 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 Vertical load acting on the abutment (P) composes of the following components S.No

1

Type of load

Intensity in KN


699.20KN


386.51KN


-161.04KN

2

Net self weight

3


Eccentricty about x- Eccentricty about yaxis(m) axis(m) -0.74

0.00

225.46KN

0.210

0.000

203.63KN

0.430

0.000


Type of load

Intensity in KN

Direction x or y


1

Wind load

16.50KN

x-Direction

4.33

2


0.00KN

y-Direction

0.00

3

Water current force

0.62KN

x-Direction

3.17

4


152.54KN

y-Direction

0.72

5


247.50KN

y-Direction

0.40

Check for stresses:About x-axis:Breadth of 1st footing b = Depth of 1st footing d = Area of the footing = A =

6.25m 2.30m 14.375 m2

Section modulus of bottom footing about x-axis --Zx =

(1/6)bd2 =

5.51 m3


1 2 3 4 5

Type of load


S.No

1 2 3 4 5

Intensity in KN (P)

Type of load

Stress at heel =

P/A(1+6e/b)+M/Z =


699.20KN 225.46KN 203.63KN

-0.74 0.21 0.43

14.09 18.85 20.01

152.54KN 247.50KN

0.72 0.40

-19.89 18.0 51.03

Intensity in KN (P)



Eccentricity


699.20KN 225.46KN 203.63KN

0.74 -0.21 -0.43

83.19 12.52 8.32

152.54KN 247.50KN

0.72 0.40

19.89 -18.0 105.95



P/A(1+6e/b)+M/Z =

Hence safe.

About y-axis:-


Breadth of 1st footing b = Depth of 1st footing d = Area of the footing = A =

2.30m 6.25m 14.375 m2

Section modulus of bottom footing about y-axis --Zy =

(1/6)bd2 =

14.97 m3


1 2 3 4 5

S.No

1 2 3 4 5

Type of load

Intensity in KN (P)

Vertical loads:-(Stress = P/A(1+6e/b) Reaction due to dead load from super structure Net self wieght of abutment&footings Vertical component of Earth pressure Horizontal loads:- (Stress = M/Z) Wind load Water current force

Type of load


P/A(1+6e/b)+M/Z =


699.20KN 225.46KN 203.63KN

0.00 0.00 0.00

48.64 15.68 14.17

16.50KN 0.62KN

4.33 3.17

-4.77 -0.1 73.59

Intensity in KN (P)



Eccentricity


699.20KN 225.46KN 203.63KN

0.00 0.00 0.00

48.64 15.68 14.17

16.50KN 0.62KN

4.33 3.17

4.77 0.1 83.39



P/A(1+6e/b)+M/Z =


Hence safe.

V)Check for stability of abutments:a)Load Envelope-III:-(The Canal is dry,back fill intact with live load on span) 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 Vertical load acting on the abutment (P) composes of the following components S.No

Type of load

Intensity in KN


1


699.20KN

0.82

0.00

2

Self wieght of abutments

295.42KN

0.270

0.000

3

Reaction due to live load with impact factor

466.66KN

0.82

0.000

4

Vertical component of Active Earth pressure

203.63KN

0.430

0.00

1664.91KN


Type of load

Intensity in KN

Direction x or y


1

Wind load

16.50KN

x-Direction

4.33

2


58.69KN

y-Direction

4.33

3

Horizontal Active Earth pressure force

152.54KN

y-Direction

0.72

227.73KN 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 =

254.11Kn-m

Moment due to active earth pressure force =

109.60Kn-m

Total overturning moment =

363.70Kn-m

Taking moments of all the restoring forces about toe of the abutment wrt x-axis,, Moment due to self weight of abutment =

375.18Kn-m

Moment due to live load reaction on abutment =

846.99Kn-m

Moment due to super structure load reaction on abutment =

1269.04Kn-m

Moment due to vertical component of active earth pressure =

291.19Kn-m

Total Restoring moment =

Factor of safety =

7.65017071

> 2.0

2782.40Kn-m

Hence safe

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

Check for stability against sliding:Total vertical load acting on the base of the abutment Vb =

1664.91KN

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

227.73KN

Coefficient of friction between concrete surfaces = Factor of safety against sliding Fs =

0.80

5.84879451 > 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) 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 Vertical load acting on the abutment (P) composes of the following components S.No

1

Type of load

Intensity in KN


699.20KN

Self wieght of abutments

295.42KN


-123.10KN

2

Net self wieght

3

Vertical component of Active Earth pressure

Eccentricty about x- Eccentricty about yaxis(m) axis(m) 0.82

0.00

172.32KN

0.270

0.000

203.63

0.430

0.00


Type of load

Intensity in KN

Direction x or y


1

Wind load

16.50KN

x-Direction

4.33

2


0.00KN

y-Direction

0.00

3

Active Earth pressure force

152.54KN

y-Direction

0.72

4

Force due to water pressure

247.50KN

y-Direction

0.40

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 = Moment due to active earth pressure force =

0.00Kn-m 109.60Kn-m

Total overturning moment =

109.60Kn-m

Taking moments of all the restoring forces about toe of the abutment wrt x-axis, Moment due to self weight of abutment =

218.85Kn-m

Moment due to water pressure force on the abutment =

99.00Kn-m

Moment due to super structure load reaction on abutment =

1269.04Kn-m

Moment due to vertical component of active earth pressure =

291.19Kn-m

Total Restoring moment =

Factor of safety =

17.1362919

1878.08Kn-m

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

Check for stability against sliding:Total vertical load acting on the base of the abutment Vb =

623.45KN

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

152.54KN

Coefficient of friction between concrete surfaces = Factor of safety against sliding Fs =

3.26968769 > 1.5 Hence safe (As per clause 706.3.4 of IRC:78-2000)

0.80

DESIGN OF RAFT FOR THE SLAB CULVERT Name of the work:-Slab culvert on 6/0 Km of Vemuladeevi Channel Abutment Abutment

Length of the Raft:-

=

14.60m

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 = Footing-II = Wt.of abutments =

182.16Kn 194.04Kn 590.84Kn

Total Dead load stress =

23.65Kn/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 1.2

6.8 4.3

6.8 3.0

5.475

2365.43Kn

0.625

14.60m

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

2.99m

Centre of gravity from the end of raft =

3.615m

Eccentricity =

3.685m

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

15.08Kn/Sqm

Min.stress =

-7.95Kn/Sqm

Total stress due to dead load and live load Max.Stress =

38.73Kn/Sqm

Min.Stress =

15.70Kn/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 =

3.60Kn/Sqm

Hence,the Max.stress on the soil =

59.83Kn/Sqm Which is less than 6t/sqm(Soil testing report)

Hence safe. Net Max.upward pressure acting on Raft =

38.73Kn/Sqm

Net Min.upward pressure acting on Raft =

15.70Kn/Sqm

The design stress =

27.22Kn/Sqm

Hence,the UDL on the raft =

27.22Kn/m

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

1.375

11.85

1.375

UDL of 27.22Kn/m After analysis the bending moment diagram is as given below:

678

38.6

Max.Negative bending moment Mu =

678.00KNm

Max.Positive bending moment Mu =

38.60KNm

Effective depth required d = Over all depth provided =

Mu/0.138fckb =

443.31mm

700.00mm

Effective depth provided(Assuming 40mm cover) d =

637.50mm

Top steel:Mu/bd2 =

1.668

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

0.505 3219.38sqmm

Bottom steel:Mu/bd2 =

0.095

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

0.12 765.00sqmm

Hence provide 12mm dia HYSD bars@ 125mm c/c spacing at bottom and provide 25mm bars at 150mm c/c at top Hence Ast provided at top = Hence Ast provided at bottom =

3270.83sqmm 904.32sqmm

Provide distribution reinforcement of 0.12% both at top and bottom Area =

840.00sqmm

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

Hydraulic design Hydraulic Particulars:1.Full supply Level

1.488

2.Ordinary Flood level 3.Lowest Bed level

0.488

4.Average bed slope (1 in 17000)

0.000059

5.Rugosity Coefficient(n) (As per table 5 of IRC:SP 13)

0.025

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

0.509

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

1.997

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

2.862

8.Width of carriage way

5.500

Discharge Calculations:1)From the data furnished by the Irrigation Department:Design discharge =

3.300Cumecs

2)Area Velocity method:Depth of flow w.r.t HFL =

1.000m

Bed width =

8.30m

Assuming side slopes 1:1.5 in clayey soils,top width at HFL = Wetted Area =

9.05sqm

Wetted perimetre =

11.13m

Hydraulic Radius

R=

Velocity V =

1/nX(R2/3XS1/2)

Discharge Q =

AXV

Design Discharge = Design Velocity =

9.800m

Total area/Wetted perimeter =

0.81 0.27m/sec 2.44Cumecs 3.300Cumecs 0.337m/sec

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. Hence,as per Lacey's silt theory,the regime width W = 4.8Q 1/2 = 4.8*3.30.5 =

8.72m

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 = Width of channel at H.F.L(b+h) = Clear span = Effective linear water way = di = Depth of flow =

0.15m 9.80m 10.00m 10.00m 1.00m

Head due to velocity of approach =

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

0.004m

Combined head due to Velocity of approach and afflux

hi =

0.154m

Velocity through vents

0.90X(2ghi)1/2 =

Vv =

Linear water way required

LWW = Qd/(VvXdi) =

No.of vents required =

LWW /LC

1.56m/sec 2.11m

=

0.211 Say---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=

0.98

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 =

Lacey's Silt factor ' f ' = 1.76Xm1/2(For normal silt) = Discharge per metre width of foundations = q =

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

Maximum scour depth Dm = 1.5XD =

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

Bottom level of foundation =

Depth of foundation below low bed level = The Minimum Safe Bearing capacity of the soil is considered as 60 KN/m2 at a depth of 2.00m below LBL Hence open foundation in the form of raft is proposed at a depth of 2.0m below LBL,ie,at a level of Cut-off walls and aprons are not required from scour depth point of view

uly alluvial in nature.

ced scour

o ensure adequate

4.39Cumecs

1.00 0.439

0.78m

1.17m

2.37m

-0.88m

1.370m

-1.512m

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