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

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:-

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

Step2:-

The vertical clearence and afflux are verified.

below the maximum scour depth

Step3:-

The structural components are desined in the following manner:-

and culverts of medium importance is selected.

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

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

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

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

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

c.Ventway calculations are done for fixation of ventway.

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

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

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

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

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

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

d.The structural components like Abutment,raft foundation are

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

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

Design of Abutments

I)Design Parameters:-

Clear Right Span = 4.00m

= 4.740m

Width of the carriage way = 5.50m

= 0.395m

= 0.075m

= 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

(As per hydralic calculations)

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

= 0.15m

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

= 1.65m

= 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 = 6.75m

= 0.40m

Type of bearings = No bearings proposed

Deck slab length

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

Thickness of wearing coat

Height of railing

Canal side offset of 1st footing wrt abutment

Width of 2nd footing

Thickness of 2nd footing

Canal side offset of 2nd footing wrt abutment

Thickness of VRCC RAFT footing

= 25KN/cum

= 24KN/cum

= 18KN/Cum

= 10KN/Cum

= 30

= 72.86

= 0

= 15

= 1.20m

= 2.605m

= 0.785m

= 1.705m

= -0.815m

= 6.50t/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 = 128.72KN

Unit weight of RCC (yrc

)

Unit weight of PCC (ypc

)

Density of back fill soil behind abutments (y)

Unit weight of water (yw)

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 (f

ck)

Yield strength of steel (fy)

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

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

W1W1

S.No Description Load in KN

1 55.539 0.86

2 150.282 0.345

3 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


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


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

Distance of centroid of load from toe of abutment

Back batter(W1)

Centre portion(W2)

Front batter(W3)

Distance of centroid of load from toe of 1st 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


Eccentricity = 0.015m

xii)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 3rd footing


1 Back batter 0 1.162 Centre portion 0 0.6453 Front batter 0 0.34 1st footing 0 0.605 2nd footing 0 0.536 3rd footing 0 0.00

0



2.Live Load:-

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

Distance of centroid of load from toe of 2nd footing

Distance of centroid of load from toe of 3rd footing

GENERAL IRC Class-A loading Pattern

are to be designed for IRC Class A loading.2.

7t

2.7

t

11.4

t

11.4

t

6.8

t

6.8t

6.8

t

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 3802.7 150 200

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

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) =

Y

X

11.4t

11.4t

475

5500

Portion to be loadedwith 5KN/m² liveload

5380

35252925

4000

6052.7t

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 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 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

Wheel Load/UDL in KN

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


Y

X

Location of Resultant

3637

2402

Calculation of reactions on abutments:-

238.88KN

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,

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.

Reaction due to loads Ra =

Reaction due to point loads = Rb =

Y

X


3637

2402

300

300

205

415

415

340

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

Height of the deck system = 1.670

Breadth of the deck system = 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 =

Kg/m2.

5.Water current force:-

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

17.94

(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

P = 52KV2 = Kg/m2.

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

'2Sin(a+Q)

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

sin(a+b)

Sin(a+Q) = SIN[3.14*(72.86+30)/180] = 0.975Sin(a-q) = SIN[3.14*(72.86-15)/180] = 0.846Sina = SIN[3.14*(72.86)/180] = 0.955Sin(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*(72.86+0)/180] = 0.955

From the above expression,

0.45

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

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

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

Ka =

Ka =

Surcharge load = 9.72 KN/sqm

9.72

1.650

13.37 9.72

Area of the rectangular portion = 16.04Area of the triangular portion = 11.03

27.07

Taking moments of the areas about the toe of the wall

S.No Description Area Lever arm Moment

1 Rectangular 16.04 0.825 13.2332 Triangular 11.03 0.55 6.0665

27.07 19.2995

Height from the bottom of the wall = 0.71m

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

0.70

32.141.650m

0.71m

72.86

1.200.22

Total earth pressure acting on the abutment P = 148.88KN

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

Horizontal component of the earth pressure Ph =

Vertical component of the earth pressure Pv =

BFL -0.815m

25.20kn/sqm

Total horizontal water pressure force = 174.64KN

The above pressure acts at height of H/3 = 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

S.No Type of load Intensity in KN

1 Reaction due to dead load from super structure 198.54KN -0.340

2 Self wieght of abutment&footings 330.56KN 0.015

3 338.96KN -0.340

4 Impact load 0.00 0.00

868.07

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

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

Eccentricty about x-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

m2

Section modulus of bottom footing 2.93

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 198.54KN -0.3402 Self wieght of abutment&footings 330.56KN 0.0153 Reaction due to live load with impact factor 338.96KN -0.3404 Impact load 0.00KN 0.000

Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 35.34KN 4.22

S.No Type of load Eccentricity

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.3402 Self wieght of abutment&footings 330.56KN -0.0153 Reaction due to live load with impact factor 338.96KN 0.3404 Impact load 0.00KN 0.000


Stress at heel = P/A(1+6e/b)+M/Z = 15.08 KN/Sqm>-2800KN/sqm.

Hence safe.

Stress at toe = P/A(1+6e/b)+M/Z = 148.06 KN/Sqm<5000KN/sqm

Hence safe.

About y-axis:-

Breadth of 3rd footing b = 1.65m

Depth of 3rd footing d = 6.45m

Area of the footing = A = 10.6425

(1/6)bd2 = m3

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

For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2

Intensity in KN (P)

Eccentricity/Lever arm

Intensity in KN (P)

m2

Section modulus of bottom footing about = 11.44

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 198.54KN 0.002 Self wieght of abutment&footings 330.56KN 0.003 Reaction due to live load with impact factor 338.96KN 0.0004 Impact load 0.00KN 0.00

Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.526 Water current force 0.33KN 3.02

S.No Type of load



Stress at up stream side P/A(1+6e/b)+M/Z = 74.96 KN/Sqm>-2800KN/sqm.edge =

Hence safe.

Stress at down stream side P/A(1+6e/b)+M/Z = 88.18 KN/Sqm<5000KN/sqmedge =

Hence safe.

i)On top of 2nd footing


(1/6)bd2 = m3



Intensity in KN (P)


Intensity in KN (P)






2 Self wieght of abutment&cut waters 265.22KN 0.090

3 Reaction due to live load with impact factor 338.96KN -0.340







About x-axis:-

Breadth of 1st footing b = 6.45mDepth of 1st footing d = 1.50mArea of the footing = A = 9.675

Section modulus of base of abutment 2.42

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)

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


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

m2

(1/6)bd2 = m3



Intensity in KN (P)


1 Reaction due to dead load from super structure 198.54KN -0.342 Self wieght of abutment&footings 265.22KN 0.093 Reaction due to live load with impact factor 338.96KN -0.344 Impact load 0.00KN 0.00



Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.342 Self wieght of abutment&footings 265.22KN -0.093 Reaction due to live load with impact factor 338.96KN 0.344 Impact load 0.00KN 0.00



Hence safe.


Hence safe.

About y-axis:-



about y-axis--Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

Intensity in KN (P)

m2

(1/6)bd2 = m3


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

S.No Type of load



S.No Type of load



Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 76.19 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<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


1 Reaction due to dead load from super structure 198.54KN -0.4152 Self wieght of abutment&footings 205.82KN 0.120

Intensity in KN (P)


Intensity in KN (P)




3 Reaction due to live load with impact factor 338.96KN -0.415



1 Wind load 16.50KN x-Direction2 Tractive,Braking&Frictional resistance of bearings 35.34KN y-Direction3 Water current force 0.33KN x-Direction


About x-axis:-

Breadth of abutment b = 6.45mDepth of abutment d = 1.20mArea of the footing = A = 7.74


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 198.54KN -0.4152 Self wieght of abutment&footings 205.82KN 0.1203 Reaction due to live load with impact factor 338.96KN -0.4154 Impact load 0.00KN 0.00



Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.4152 Self wieght of abutment&footings 205.82KN -0.120


m2

(1/6)bd2 = m3



Intensity in KN (P)


Intensity in KN (P)

3 Reaction due to live load with impact factor 338.96KN 0.4154 Impact load 0.00KN 0.00


Stress at heel = P/A(1+6e/b)+M/Z = -10.92 KN/Sqm>-2800KN/sqm.

Hence safe.


Hence safe.

About y-axis:-

Breadth of abutment b = 1.20mDepth of abutment d = 6.45mArea of the footing = A = 7.74


about y-axis--Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



S.No Type of load

m2

(1/6)bd2 = m3



Intensity in KN (P)


Intensity in KN (P)






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






Self wieght of abutment&cut waters 330.56KN

Reduction in self weight due to buoyancy -137.72KN

2 Net self weight 192.84KN 0.015

3 Vertical component of earth pressure 79.17KN 0.380








4 Horizontal load due to earth pressure 126.09KN y-Direction

5 Water pressure force 174.64KN y-Direction


About x-axis:-

Breadth of bottom footing b = 6.45mDepth of bottom footing d = 1.65mArea of the footing = A = 10.6425


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 198.54KN -0.342 Net self wieght of abutment&footings 192.84KN 0.013 Vertical component of Earth pressure 79.17KN 0.38

Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 126.09KN 1.315 Water pressure force 174.64KN 0.84


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.342 Net self wieght of abutment&footings 192.84KN -0.013 Vertical component of Earth pressure 79.17KN -0.38



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 = 1.65mDepth of bottom footing d = 6.45mArea of the footing = A = 10.6425


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 198.54KN 0.002 Net self wieght of abutment&footings 192.84KN 0.003 Vertical component of Earth pressure 79.17KN 0.00






m2

(1/6)bd2 = m3



Intensity in KN (P)


Intensity in KN (P)


Hence safe.

ii)On top of 2nd footing






Self wieght of abutment&footings 330.56KN











About x-axis:-

Breadth of 2nd footing b = 6.45mDepth of 2nd footing d = 1.50mArea of the footing = A = 9.675




m2


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 198.54KN -0.342 Net self wieght of abutment&footings 192.84KN 0.013 Vertical component of Earth pressure 79.17KN 0.38






Hence safe.


Hence safe.

About y-axis:-



(1/6)bd2 = m3



Intensity in KN (P)


Intensity in KN (P)

m2

(1/6)bd2 = m3

about y-axis --Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load








Hence safe.

iii)On top of 1st footing






Intensity in KN (P)


Intensity in KN (P)



Self wieght of abutment&cut waters 265.22KN











About x-axis:-



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 198.54KN -0.34




m2

(1/6)bd2 = m3



Intensity in KN (P)


2 Net self wieght of abutment&footings 154.71KN 0.093 Vertical component of Earth pressure 79.17KN 0.38






Hence safe.


Hence safe.

About y-axis:-



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 198.54KN 0.002 Net self wieght of abutment&footings 154.71KN 0.00

Intensity in KN (P)

m2

(1/6)bd2 = m3



Intensity in KN (P)


3 Vertical component of Earth pressure 79.17KN 0.00Horizontal loads:- (Stress = M/Z)

4 Wind load 16.50KN 3.925 Water current force 0.33KN 2.42




Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 48 KN/Sqm>-2800KN/sqm.


Hence safe.

V)Check for stability of abutments:-

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





1 Reaction due to dead load from super structure 198.54KN 0.415

2 Self wieght of abutments 205.79KN 0.120

3 Reaction due to live load with impact factor 338.96KN 0.415

4 Vertical component of Active Earth pressure 79.17KN 0.380

822.46KN

Intensity in KN (P)






3 Horizontal Active Earth pressure force 126.09KN y-Direction

177.92KN

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 live load reaction on 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 = 3.376949592 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)

Check for stability against sliding:-

Coefficient of friction between concrete surfaces =


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

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

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)





1 Reaction due to dead load from super structure 198.54KN 0.415

Self wieght of abutments 205.79KN

-85.70KN

2 Net self wieght 120.09KN 0.120

3 Vertical component of Active Earth pressure 79.17 0.380




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 =

Factor of safety against sliding Fs =



Reduction in self weight due to buoyancy


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:-

Coefficient of friction between concrete surfaces =

2.372288897 > 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 Abutments

No bearings 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

0000000

2.7t

2.7

t

11.4

t

11.4

t

6.8

t

6.8t

6.8

t

6.8t

1.10

1.80

3.20 1.20 4.30 3.00 3.00 3.00

is severe and the same is to be considered as per

Y

X

11.4t

11.4t

475

5500

Portion to be loadedwith 5KN/m² liveload

5380

35252925

4000

6052.7t

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

Y

X


3637

2402

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

Y

X


3637

2402

0.2095

2.65KN

16.50KN

4.52m

3.02m

4.22m

1.650m

13.37KN/sqm

126.09KN

79.17KN

0.38m

0.00

0.000

0.000

0.00

4.52

4.22

3.02

Eccentricty about y-axis(m)

composes of the following components

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

12.7631.4921.78

0

-50.95

15.08

24.5630.6341.92

0

50.95

148.06

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm

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

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

18.6631.0631.85

0

-6.52-0.09

74.96

18.6631.0631.85

0

6.520.09

88.18

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm

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

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

0.00

0.000

0.000

0.00

4.22

3.92

2.72





14.0328.9423.95

0

-57.27

9.65

27.0125.1246.12

0

57.27

155.52

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm


20.5227.4135.04

0

-6.69-0.09

76.19

20.5227.4135.04

0

6.690.09

89.75

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm

0.000.000




0.000

0.00

3.923.622.42

15.7529.0726.89

0

-82.63

-10.92

35.5523.62





60.70

82.63

202.5

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm

25.6526.5943.79

0

-7.77-0.1

88.16



25.6526.5943.79

0

7.770.1

103.9

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm

0.00

0.000

0.000

4.52




0.00

3.02

1.31

0.84

12.7618.3710.07

-56.5650.1

34.76

24.5617.874.81

56.56-50.153.68

KN/Sqm>-2800KN/sqm.



KN/Sqm<5000KN/sqm

18.6618.127.44

-6.52-0.1

37.61

18.6618.127.44

6.520.1

50.83

KN/Sqm>-2800KN/sqm.

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


KN/Sqm<5000KN/sqm

0.00

0.000

0.000

4.22

0.00

2.72

1.01

0.54




14.0320.2111.08

-52.839.0

31.51

27.0119.655.29

52.8-39.065.76

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



20.5219.938.18

-6.69-0.1

41.85

20.5219.938.18

6.690.1

55.41

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



0.00

0.000

0.000

3.92

0.00

2.42

0.71

0.24

17.54





21.6613.84

-58.0727.1

22.05

33.7618.326.61

58.07-27.189.68

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm

25.6519.99



10.23

-7.77-0.148

25.6519.9910.23

7.770.1

63.74

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm

0.00

0.000

0.000

0.00



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


822.46KN

177.92KN

0.80




0.00

0.000

0.00

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


373.89KN

126.09KN

0.80


DESIGN OF RAFT FOR THE SLAB CULVERT

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 = 118.80KnFooting-II = 130.68KnWt.of abutments = 411.58Kn

Total 1058.14Kn

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

Name of the work:-Construction of Slab culvert on the R/f R&B Road to Sariapalli SC colony

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


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 = 7.20Kn/Sqm

Hence,the Max.stress on the soil = 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 loadingas 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 = 185.97mm

Over all depth provided = 400.00mm

Effective depth provided(Assuming 40mm cover) d = 337.50mm

Top steel:-

1.01

From table 3 of SP 16,percentage of steel required = 0.245

Area of steel required = 826.88sqmm

Bottom steel:-

0.177

From table 3 of SP 16,percentage of steel required/Minimum steel = 0.15


Mu/0.133f

ckb =

Mu/bd2 =

Mu/bd2 =

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

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

Hence Ast provided at top =

Hence Ast provided at bottom =

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

Hydraulic design

Hydraulic Particulars:-

1.Full supply Level 1.705

2.Ordinary Flood level

3.Lowest Bed level 0.785

4.Average bed slope 0.000067(1 in 15000)

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

6.Vertical clearence proposed 0.430(As per clause 15.5 of IRC:SP 13&as per profile)

6.Bottom of deck proposed 2.135(MFL+Vertical clearence)

7.Road Crest level 2.605(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 = 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 = 3.880m

Wetted Area = 2.93sqm

Wetted perimetre = 5.10m

Hydraulic Radius R= Total area/Wetted perimeter = 0.58

Velocity V = 0.23m/sec

Discharge Q = AXV 0.68Cumecs

Design Discharge = 0.680Cumecs

5.Rugosity Coefficient(n)

1/nX(R2/3XS1/2)

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.

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 = 0.15m3.88m

Clear span = 4.00mEffective linear water way = 4.00m

Depth of flow = 0.92m

Head due to velocity of approach = 0.002m

Combined head due to Velocity of approach and 0.152mafflux

1.55m/sec

Linear water way required 0.48m

No.of vents required = = 0.12Say---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 =

Hence,as per Lacey's silt theory,the regime width W = 4.8Q1/2 = 4.8*0.680.5 =

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

di =

(Vmax

2/2g)X[di/(d

i+x)]2

hi =

Velocity through vents Vv = 0.90X(2gh

i)1/2 =

LWW

= Qd/(V

vXd

i) =

LWW

/LC

Discharge per metre width of foundations = q =

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

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

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 =

Hydraulic design

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

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

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

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 =

(in clock wise direction)

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 =

Coefficient of active earth pressure by Coulomb's theory

Sin(a+Q)

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

sin(a+b)

From the above expression,

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 toSurcharge load = 324

324

2.420m

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) =

Ka =

Ka =

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

0.94m2.420

900.30

Design of wall :-

Factored bending moment Mu = 10709.98Kgm

Effective depth required d = 179.47mm

Over all depth provided = 300.00mm

Effective depth provided(Assuming 40mm cover) d = 252.00mm

1.687

From table 2 of SP 16,percentage of steel required = 0.421


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

1130.40sqmm

Check for shear:-

Percentage of tension steel = 0.45

Horizontal component of the earth pressure Ph =

Vertical component of the earth pressure Pv =

Mu/0.133f

ckb =

Mu/bd2 =

Hence Ast provided =

Maximum shear force on the member = 57.12KN

Factored Design shear force = 85.68KN

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 7

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 1.5

Hence,the ratio is 10.5

The effective depth required = 0.24 <0.252 (Actually provided)

Nominal shear stress tv =V

u/bd =

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

DESIGN OF FLY WINGS

2.420m2.420m0.00m

1800Kg/CumM25

Fe500

3090

015

0.60m

25N/sqmm500N/sqmm

2.50m

0.30m0.15m

2

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

1306.80Kg/sqm

2284.80Kg/m

611.88Kg/m

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

(Actually provided)

design of 4m span rcc slab culvert

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