Design of 4m span RCC slab culvert

Construction of 4.00mts span culvert Name of the work:-R/f R&B Road to Sariapalli SC colony

Construction of 4.00mts span culvert

me of the work:-R/f R&B Road to Sariapalli SC colony

Design Philosophy:-

The design of 1V-- 4.37m 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 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

=

4.00m

Deck slab length

=

4.740m

Width of the carriage way

=

5.50m

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

=

0.395m

Thickness of wearing coat

=

0.075m

Height of railing

=

1.200m

Thickness of dirt wall

=

0.30m

Sectional area of dirt wall

=

0.330sqm

Thickness of RAFT footing

=

0.40m

Height of abutments

=

1.650m

Top width of abutments

=

0.690m

Bottom width of abutments

=

1.20m

Sectional area of abutment section

=

1.559sqm

Bank side batter of abutment

=

0.510m

Stream side batter of abutment

=

0.000m

Width of 1st footing

=

1.50m

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

=

1.65m

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

=

6.75m

Thickness of VRCC RAFT footing

=

0.40m

Type of bearings

=

(As per hydralic calculations)

No bearings proposed

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

Angle of shearing resistance of back fill material(Q)

=

30

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

=

72.86

Slope of back fill (b)

=

0

Angle of wall friction (q)

=

15

Height of surcharge considered (h3)

=

1.20m

Road crest level (RTL)

=

2.605m

Low bed level (LBL)

=

0.785m

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

= =

1.705m -0.815m

=

6.50t/sqm

Compressive strength of concrete for RCC Raft 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 =

128.72KN

ii)Self wieght of dirtwall over abutment =

45.38KN

iii)Self weight of wearing coat =

24.44KN

198.54KN 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 =

205.79KN

v)Self wieght of top footing =

59.40KN

vi)Self wieght of 2nd footing =

65.34KN

vii)Self wieght of 3rd footing =

0.00KN

viii)Self wieght of 4th footing =

0.00KN

330.53KN

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

1

Back batter(W1)

55.539

0.86

2

Centre portion(W2)

150.282

0.345

3

Front batter(W3)

0

0

205.821 Location of resultant from toe of abutment =

0.48m

Eccentricity wrt centre of base of abutment =

0.120m

x)Calculation of eccentricity of self weight of abutment&1st footing w.r.t bottom of 1st footing S.No

Description Load in KN

Distance of centroid of load from toe of 1st footing

1

Back batter

55.539

1.01

2

Centre portion

150.282

0.495

3

Front batter

0

0

4

1st footing

59.40KN

0.75

265.221 Location of resultant from toe of abutment =

0.66m

Eccentricity wrt centre of 1st footing=

0.090m

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

S.No

Description Load in KN

Distance of centroid of load from toe of 2nd footing

1

Back batter

55.539

1.16

2

Centre portion

150.282

0.645

3

Front batter

0

0.3

4

1st footing

59.40KN

0.900

5

2nd footing

65.34KN

0.825

330.561 Location of resultant from toe of abutment =

0.81m

Eccentricity =

0.015m

xii)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 3rd footing S.No

1 2 3 4 5 6

Description Load in KN

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

Distance of centroid of load from toe of 3rd footing

0 0 0 0 0 0 0

1.16 0.645 0.3 0.60 0.53 0.00

Location of resultant from toe of abutment =

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

6.8t

6.8t

3.00

3.00

6.8t

11.4t

3.00

6.8t

4.30

1.20

11.4t

3.20

2.7t

1.80

2.7t

1.10

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

4000

5380

Portion to be loaded with 5KN/m² live load 2.7t 605

X

5500 2925

3525

The ground contact area of wheels for the above placement,each axle wise is given below:Axle load (Tonnes) 11.4 6.8 2.7

Ground Contact Area B(mm)

W(mm)

250 200 150

500 380 200

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

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

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

1

57

0.875m

2

57

0.875m

3

57

2.675m

4

57

2.675m

5

13.5

0.875m

6

13.5

2.675m

7

14.8125

0.313m

8

83.5425

4.688m

353.355 Distance of centroid of forces from y-axis

= 2.402m Eccentricity =

0.823m

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

1

57

5.005m

2

57

5.005m

3

57

3.805m

4

57

3.805m

5

13.5

0.605m

6

13.5

0.605m

7

14.81KN

2.690m

8

83.54KN

2.690m

353.355 Distance of centroid of forces from x-axis

= 3.637m Eccentricity =

0.947m

Y

Location of Resultant

2402

3637

X

X Calculation of reactions on abutments:-

Reaction due to loads Ra =

238.88KN

Reaction due to point loads = Rb =

114.48KN

Hence,the critical reaction is Ra =

238.88KN

The corrected reaction at obtuse corner =

238.88KN

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

300 205

300

415 415 340 The eccentricty of the line of action of live load at bottom of abutment =

0.415m

----do----on top of 1st footing

=

0.415m

----do----on top of 2nd footing

=

0.340m

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

0.419

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

For the remaining portion,impact need not be considered.

4.Wind load:The deck system is located at height of (RTL-LBL)

1.82m

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 = Breadth of the deck system =

1.670 5.34

The effective area exposed to wind force =HeightxBreadth = Hence,the wind force acting at centroid of the deck system = (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 =

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

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

17.94 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 =

0.33KN

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

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 35.34KN

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

7.Buoyancy :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 =

8.57Cum

ii)Volume of top footing =

2.48Cum

iii)Volume of 2nd footing =

2.72Cum

iv)Volume of 3rd footing =

0.00Cum

v)Volume of 4th footing =

0.00Cum 13.77Cum

Reduction in self wieght =

137.72KN

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*(72.86+30)/180] = SIN[3.14*(72.86-15)/180] = SIN[3.14*(72.86)/180] = SIN[3.14*(30+15)/180] = SIN[3.14*(30-0)/180] = SIN[3.14*(72.86+0)/180] =

0.975 0.846 0.955 0.707 0.5 0.955

From the above expression, Ka =

0.45

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

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

Pa =

Surcharge load =

9.72 KN/sqm

9.72

1.650

13.37

9.72

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

16.04 11.03 27.07

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

Description

Area

Rectangular Triangular

16.04 11.03 27.07

Lever arm Moment 0.825 0.55

13.233 6.0665 19.2995

Height from the bottom of the wall =

0.71m

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

0.70

32.14 1.650m 0.71m 72.86

1.20 0.22 Total earth pressure acting on the abutment P =

148.88KN

Horizontal component of the earth pressure P h =

Vertical component of the earth pressure P v =

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 1.705m

2.52

BFL -0.815m

25.20kn/sqm

Total horizontal water pressure force = The above pressure acts at height of H/3 =

174.64KN 0.84m

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 xaxis(m)

1

Reaction due to dead load from super structure

198.54KN

-0.340

2

Self wieght of abutment&footings

330.56KN

0.015

3

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

338.96KN

-0.340

4

Impact load

0.00

0.00

868.07 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

1

Wind load

16.50KN

x-Direction

2

Tractive,Braking&Frictional resistance of bearings

35.34KN

y-Direction

3

Water current force

0.33KN

x-Direction

Check for stresses:About x-axis:Breadth of 2nd footing b =

6.45m

Depth of 2nd footing d =

1.65m

Area of the footing = A =

10.6425 m2

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

(1/6)bd2 =

2.93 m3

For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm 2 i.e, 5000KN/sqm For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm 2 i.e, -2800KN/sqm S.No

1 2 3 4 5

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 Impact load Horizontal loads:- (Stress = M/Z) Tractive,Braking&Frictional resistance of bearings

S.No

1 2 3 4 5

Intensity in KN Eccentricity/Lever (P) arm

Type of load

-0.340 0.015 -0.340 0.000

35.34KN

4.22

Intensity in KN Eccentricity (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

Stress at heel =

198.54KN 330.56KN 338.96KN 0.00KN

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

198.54KN 330.56KN 338.96KN 0.00KN

0.340 -0.015 0.340 0.000

35.34KN

4.22

15.08 KN/Sqm>-2800KN/sqm.

Hence safe. Stress at toe =

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

148.06 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:-

88.18 KN/Sqm-2800KN/sqm.

Hence safe. Stress at toe =

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

155.52 KN/Sqm-2800KN/sqm.

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

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

89.75 KN/Sqm-2800KN/sqm.

Hence safe. Stress at toe =

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

202.5 KN/Sqm-2800KN/sqm.

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

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

103.9 KN/Sqm-2800KN/sqm.

Hence safe. Stress at toe =

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

53.68 KN/Sqm-2800KN/sqm.

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

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

50.83 KN/Sqm-2800KN/sqm.

Hence safe. Stress at toe =

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

65.76 KN/Sqm-2800KN/sqm.

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

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

55.41 KN/Sqm-2800KN/sqm.

Hence safe. Stress at toe =

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

89.68 KN/Sqm-2800KN/sqm.

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

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

63.74 KN/Sqm 2.0 Hence safe (As per clause 706.3.4 of IRC:78-2000)

Factor of safety against sliding Fs =

3.698071786 > 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 Eccentricty about xaxis(m)

Reaction due to dead load from super structure

198.54KN

0.415

Self wieght of abutments

205.79KN

Reduction in self weight due to buoyancy

-85.70KN

2

Net self wieght

120.09KN

0.120

3

Vertical component of Active Earth pressure

79.17

0.380

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

2

Tractive,Braking&Frictional resistance of bearings

0.00KN

y-Direction

3

Active Earth pressure force

126.09KN

y-Direction

4

Force due to water pressure

174.64KN

y-Direction

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 =

Total overturning moment =

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

Moment due to water pressure force on the abutment =

Moment due to super structure load reaction on abutment =

Moment due to vertical component of active earth pressure =

Total Restoring moment =

Factor of safety =

4.532980823

> 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 V b =

Total sliding force,ie,horizontal load on the abutment H b = Coefficient of friction between concrete surfaces = Factor of safety against sliding Fs =

2.372288897 > 1.5 Hence safe (As per clause 706.3.4 of IRC:78-2000)

gs proposed

Moment

47.76

51.85

0

99.61

Moment

56.09

74.39 0

44.55 175.03

Moment

64.43

96.93

0

53.46

53.91

268.73

Moment

0 0 0 0 0 0 0

6.8t

6.8t

3.00

ered as per

5380

d

X

255.00KN

14.81KN 83.54KN 353.36KN

Moment

49.88KNm 49.88KNm 152.48KNm 152.48KNm 11.81KNm 36.11KNm 4.63KNm 391.61KNm 848.86KNm

Moment 285.29KNm 285.29KNm 216.89KNm 216.89KNm 8.17KNm 8.17KNm 39.85KNm 224.73KNm 1285.25KN

f Resultant

X

X

odulus in transverse

0.2095

2.65KN

16.50KN

4.52m

3.02m

4.22m

1.650m 13.37KN/sqm

126.09KN

79.17KN

0.38m

Eccentricty about yaxis(m) 0.00 0.000 0.000 0.00

g components Location(Ht.from the section considered). (m) 4.52 4.22 3.02

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

12.76 31.49 21.78 0 -50.95 15.08

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

-2800KN/sqm.

5000KN/sqm

24.56 30.63 41.92 0 50.95 148.06

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

18.66 31.06 31.85 0 -6.52 -0.09 74.96

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

-2800KN/sqm.

5000KN/sqm

18.66 31.06 31.85 0 6.52 0.09 88.18

Eccentricty about yaxis(m) 0.00 0.000 0.000 0.00

omponents Location(Ht.from the section considered). (m) 4.22 3.92 2.72

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

14.03 28.94 23.95 0 -57.27 9.65

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

-2800KN/sqm.

5000KN/sqm

27.01 25.12 46.12 0 57.27 155.52

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

20.52 27.41 35.04 0 -6.69 -0.09 76.19

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

20.52 27.41 35.04 0 6.69 0.09 89.75

-2800KN/sqm.

5000KN/sqm

Eccentricty about yaxis(m) 0.00 0.000

0.000 0.00

omponents Location(Ht.from the section considered). (m) 3.92 3.62 2.42

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

15.75 29.07 26.89 0 -82.63 -10.92

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

35.55 23.62

60.7 0 82.63 202.5

-2800KN/sqm.

5000KN/sqm

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

25.65 26.59 43.79 0 -7.77 -0.1 88.16

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

25.65 26.59 43.79 0 7.77 0.1 103.9

-2800KN/sqm.

5000KN/sqm

Eccentricty about yaxis(m) 0.00

0.000 0.000

omponents Location(Ht.from the section considered). (m) 4.52

0.00 3.02 1.31 0.84

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

12.76 18.37 10.07 -56.56 50.1 34.76

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

-2800KN/sqm.

24.56 17.87 4.81 56.56 -50.1 53.68

5000KN/sqm

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

18.66 18.12 7.44 -6.52 -0.1 37.61

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

-2800KN/sqm.

18.66 18.12 7.44 6.52 0.1 50.83

5000KN/sqm

Eccentricty about yaxis(m) 0.00

0.000 0.000

omponents Location(Ht.from the section considered). (m) 4.22 0.00 2.72 1.01 0.54

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

14.03 20.21 11.08 -52.8 39.0 31.51

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

-2800KN/sqm.

5000KN/sqm

27.01 19.65 5.29 52.8 -39.0 65.76

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

20.52 19.93 8.18 -6.69 -0.1 41.85

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

-2800KN/sqm.

5000KN/sqm

20.52 19.93 8.18 6.69 0.1 55.41

Eccentricty about yaxis(m) 0.00

0.000 0.000

omponents Location(Ht.from the section considered). (m) 3.92 0.00 2.42 0.71 0.24

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

17.54

21.66 13.84 -58.07 27.1 22.05

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

33.76 18.32 6.61 58.07 -27.1 89.68

-2800KN/sqm.

5000KN/sqm

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

25.65 19.99

10.23 -7.77 -0.1 48

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

25.65 19.99 10.23 7.77 0.1 63.74

-2800KN/sqm.

5000KN/sqm

Eccentricty about yaxis(m) 0.00 0.000 0.000 0.00

omponents Location(Ht.from the section considered). (m) 3.92 3.92 0.71

138.52Kn-m

89.89Kn-m

228.41Kn-m

148.17Kn-m

344.05Kn-m

201.52Kn-m

77.58Kn-m

771.32Kn-m

IRC:78-2000)

822.46KN 177.92KN 0.80

IRC:78-2000)

Eccentricty about yaxis(m) 0.00

0.000 0.00

omponents Location(Ht.from the section considered). (m) 3.92 0.00 0.71 0.24

0.00Kn-m 89.89Kn-m

89.89Kn-m

86.46Kn-m

41.91Kn-m

201.52Kn-m

77.58Kn-m

407.48Kn-m

IRC:78-2000)

373.89KN

126.09KN 0.80

IRC:78-2000)

DESIGN OF RAFT FOR THE SLAB CULVERT Name of the work:-Construction of Slab culvert on the R/f R&B Road to Sariapalli SC colony

Abutment Abutment

Length of the Raft:-

=

7.00m

Width of the Raft:-

=

6.75m

Total load on the Raft:Dead Load:Wt.of Deck slab =

257.44Kn

Wt.of wearing coat =

48.88Kn

Wt.of bed blocks over abutments =

90.76Kn

Wt.of abutments Footing-I = Footing-II = Wt.of abutments =

118.80Kn 130.68Kn 411.58Kn

Total Dead load stress =

22.39Kn/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

2.7

1058.14Kn

1.2

3.2

1.925

0.625

7.00m

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

1.00m

Centre of gravity from the end of raft =

1.625m

Eccentricity =

1.875m

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

20.13Kn/Sqm

Min.stress =

-5.03Kn/Sqm

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

42.52Kn/Sqm

Min.Stress =

17.36Kn/Sqm

Assuming the depth of raft as 40cm Stress due to self weight of raft =

10.00Kn/Sqm

Stress due to wieght of base concrete = Hence,the Max.stress on the soil =

7.20Kn/Sqm 59.72Kn/Sqm

Which is less than 6.5t/sqm(Soil testing report) Hence safe. Net Max.upward pressure acting on Raft =

42.52Kn/Sqm

Net Min.upward pressure acting on Raft =

17.36Kn/Sqm

The design stress =

29.94Kn/Sqm

Hence,the UDL on the raft =

29.94Kn/m

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

0.975

5.05

0.975

UDL of 29.94Kn/m After analysis the bending moment diagram is as given below:

115

20.2

Max.Negative bending moment Mu =

115.00KNm

Max.Positive bending moment Mu =

20.20KNm

Effective depth required d = Over all depth provided =

Mu/0.133fckb =

185.97mm

400.00mm

Effective depth provided(Assuming 40mm cover) d =

337.50mm

Top steel:Mu/bd2 =

1.01

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

0.245 826.88sqmm

Bottom steel:Mu/bd2 =

0.177

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

0.15 506.25sqmm

Hence provide 10mm dia HYSD bars@ 125mm c/c spacing at bottom and provide 12mm bars at 100mm c/c at top Hence Ast provided at top = Hence Ast provided at bottom =

1130.40sqmm 628.00sqmm

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

480.00sqmm

Adopting 10mm dia bars,the spacing required is =

163.54mm

Hence provide 10mm dia bars @ 150mm c/c spacing at top& bottom as distribution steel

y

Hydraulic design Hydraulic Particulars:1.Full supply Level

1.705

2.Ordinary Flood level 3.Lowest Bed level

0.785

4.Average bed slope (1 in 15000)

0.000067

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)

0.430

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

2.135

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

2.605

8.Width of carriage way

5.500

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

Nil

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

0.920m

Bed width =

2.50m

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

2.93sqm

Wetted perimetre =

5.10m

Hydraulic Radius

R=

Velocity V =

1/nX(R2/3XS1/2)

Discharge Q =

AXV

Design Discharge =

3.880m

Total area/Wetted perimeter =

0.58 0.23m/sec 0.68Cumecs 0.680Cumecs

Design Velocity =

0.230m/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*0.680.5 =

3.96m

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 3.88m 4.00m 4.00m 0.92m

Head due to velocity of approach =

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

0.002m

Combined head due to Velocity of approach and afflux

hi =

0.152m

Velocity through vents

0.90X(2ghi)1/2 =

Vv =

Linear water way required

LWW = Qd/(VvXdi) =

No.of vents required =

LWW /LC

1.55m/sec 0.48m

=

0.12 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=

0.97

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 fine 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 D m =

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 1.60m below LBL Hence open foundation in the form of raft is proposed at a depth of 1.60m 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

0.90Cumecs

0.200 0.225

0.85m

1.28m

2.48m

-0.77m

1.555m

-0.815m

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 = 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) (in clock wise direction) Slope of back fill(b) = Angle of wall friction (q) = Surcharge over the back fill in terms of height of back fill = Undrained Cohesion ( c) = 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 = Coefficient of active earth pressure by Coulomb's theory Ka =

Sin(a+Q) sina

sin(a-q)

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

From the above expression, Ka =

0.3

Hence,maximum pressure at the bottom of the wall

Pa =

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

324 324

2.420m

1306.80 Total Active earth pressure force =

2365.31

Height from the bottom of the wall =

0.94m

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

0.15

15

0.94m 2.420 90 0.30

Horizontal component of the earth pressure P h = Vertical component of the earth pressure P v =

Design of wall :Factored bending moment Mu = Effective depth required d = Over all depth provided =

10709.98Kgm Mu/0.133fckb = 300.00mm

Effective depth provided(Assuming 40mm cover) d = Mu/bd2 =

179.47mm

252.00mm

1.687

From table 2 of SP 16,percentage of steel required = Area of steel required =

1060.92sqmm

Hence provide 12mm dia HYSD bars@ 100mm c/c spacing Hence Ast provided =

0.421

1130.40sqmm

Check for shear:Percentage of tension steel =

0.45

Maximum shear force on the member = Factored Design shear force =

57.12KN

85.68KN

Nominal shear stress tv =Vu/bd =

0.34 N/sqmm

Hence section is safe from shear strength point of view The design shear strength of concrete for the above steel percentage from Table 19 of IS 456 is 0.46 N/sqmm > 0.34 Hence,no shear reinforcement is required. Provide temperature re inforcement @ 0.15% Area required =

337.50sqmm

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

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

The stress level is

272.18N/sqmm

For percentage of tension steel provided is

0.45

The modification factor for ratio of span to effective depth is Hence,the ratio is The effective depth required =

7

1.5

10.5 0.24