type design of submersible causeway

DESIGN OF VENTED SUBMERSIBLE CAUSEWAY

Name of the work:-B.T to the R/f KB Road to P.Bheemavaram

Design Philosophy:-

The design of submersible Causeway is carried out as per the procedure out

lined below:-Step1:-

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

method.Further the discharge from the surplus wier of the tank is also taken into account,while finalising the design discharge.The surplus wier is treated as broad-crested wier and height of fall is locally enquired.The discharge is arrived using broad crested wier formula.

Step2:-

the causeway is kept below the HFL,so that the obstruction to flow is less than 70%, when the flow is at RTL.Further,when the flow is at HFL,the obstruction to flow is kept below 30%.All the above ventway calculations are done as per IRC SP:82--2008.

calculations are carried out.

below the maximum scour depth

Step3:-

dimensions of the bridge are finalised.

The structural components are desined in the following manner:-

and culverts of medium importance is selected.

Additional live load due to silt is considered on the deck slab as per IRC SP:82--2008.

a.Discharge of the stream is arrived using area-velocity method and catchment area

a.Hydraulic particulars like HFL,OFL are fixed as per the local enquiry.

b.It is proposed to design the structure as vented submersible causeway.RTL of

c.After finalisation of design discharge,RTL and ventway calculations,afflux

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 RTL,bottom of foundation level and required ventway,the

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

b.The effect of drag and lift is considered on the causeway as per IRC-SP:82--2008.

c.Load combinations and remaining loads are selected as per IRC 6:2000

d.Stainless steel anchor bars and VRCC thrust blocks are proposed as per

IRC SP:82--2007 to safeguard against lift and drag forces respectively.

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

e.Based on the soil test reports,indivdual foundations are proposed for an SBC of 15t/m2.

f.The structural components like Abutments,piers,face walls,strip foundation are

g.The deck slab is proposed as per the drawings given in Plate No.7.09 of IRC:SP20-2002(Rural roads manual)

h.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 for causeway

I)Design Parameters:-

Clear Right Span = 6.00m

= 6.800m

Width of the carriage way = 6.00m

Thickness of deck slab as per IRC SP 20 = 0.480m

= 0.075m

Height of guard stones = 0.750m

Thickness of dirt wall = 0.30m

Sectional area of dirt wall = 0.370sqm

Thickness of strip footing = 0.45m

Height of abutments = 1.200m

(As per hydralic calculations)

Top width of abutments = 0.750m

Bottom width of abutments = 1.05m

Sectional area of abutment section = 1.080sqm

Bank side batter of abutment = 0.000m

Stream side batter of abutment = 0.300m

Width of 1st footing = 1.35m

Thickness of 1st footing = 0.30m

= 0.15m

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

= 1.50m

= 0.30m

= 0.30m

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

Width of 3rd footing = 1.65m

Thickness of 3rd footing = 0.30m

Canal side offset of 3rd footing wrt abutment = 0.45m

Bank side offset of 3rd footing wrt abutment = 0.15m

Width of VRCC strip footing = 1.95m

= 0.45m

= 0.60m

= 0.30m

Offset of top footing along width = 0.00m

Offset of 2nd footing along width = 0.00m

Offset of 3rd footing along width = 0.00m

Deck slab length

Thickness of wearing coat

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 strip footing (d3)

Canal side offset of RCC strip footing wrt abutment (s5)

Bank side offset of RCC strip footing wrt abutment (s6)

= 0.15m

Type of bearings = No bearings proposed

= 25KN/cum

= 24KN/cum

= 18KN/Cum

= 10KN/Cum

= 30

= 90

= 0

= 15

= 1.20m

= 5.645m

= 3.965m

= 6.235m

= 2.315m

= 15.00t/sqm

= 20.00N/sqmm

= 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 submersible 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

Apart from the above forces,the following pressures are to be considered as per clause 7.11.2.2 of IRC SP:82---2007:-

(a) Pressure due to static head due to afflux on upstream side and trough of standing wave on down stream side:

(b) Pressure due to velocity head

(c) Pressure due to eddies

Offset of RCC strip footing along width (w1)

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 PCC (fck)

Compressive strength of concrete for VRCC (fck)

Yield strength of steel (fy)

(d) Pressure due to friction of water against piers and bottom of slab

(e) Force due to uplift under superstructure

super structure should also be considered:

As per clause 202.3 of IRC 6:2000,the increase in permissible stresses is not permissible for theabove loading combination.

III)Loading on the submersible bridge for design of abutments:-

1.Dead Load:-

i)Self wieght of the deck slab = 244.80KN

ii)Self wieght of dirtwall over abutment = 55.50KN

iii)Self weight of wearing coat = 38.25KN

338.55KN

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 = 155.52KN

v)Self wieght of top footing = 58.32KN

vi)Self wieght of 2nd footing = 64.80KN

vii)Self wieght of 3rd footing = 71.28KN

viii)Self wieght of 4th footing = 0.00KN

349.92KN

As per the clause 7.11.3.4 of IRC:SP82--2007,Additional load of 150 mm thick silt with density equal to 15 kN/m 3 spread over the entire soffit(in case of box girders) and deck slabs of all types of

W1

W2

W3

b1

b2 b1 b3

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

S.No Description Load in KN Moment

1 0 1.05 0

2 129.6 0.675 87.48

3 25.92 0.2 5.18

155.52 92.66

Location of resultant from toe of abutment = 0.60m

Eccentricity wrt centre of base of abutment = 0.075m

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


1 Back batter 0 1.2 0

2 Centre portion 129.6 0.825 106.92

3 Front batter 25.92 0.35 9.07

4 1st footing 58.32 0.675 39.37

213.84 155.36


Eccentricity wrt centre of 1st footing= 0.055m

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

W1

W2

W3

b1

b2 b1 b3

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


1 Back batter 0 1.35 0

2 Centre portion 129.6 0.975 126.36

3 Front batter 25.92 0.5 12.96

4 1st footing 58.32 0.83 48.11

5 2nd footing 64.8 0.75 48.6

278.64 236.03


Eccentricity = 0.100m

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


1 Back batter 0 1.35 02 Centre portion 129.6 0.975 126.363 Front batter 25.92 0.5 12.964 1st footing 58.32 0.83 48.115 2nd footing 64.8 0.75 48.66 3rd footing 71.28 0.83 58.81

349.92 294.84



2.Live Load:-

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

GENERAL IRC Class-A loading Pattern

Distance of centroid of load from toe of 2nd footing

Distance of centroid of load from toe of 3rd footing

are to be designed for IRC Class A loading.

2.7t

2.7t

11.4

t

11.4

t

6.8t

6.8t

6.8t

6.8t

1.10

1.80

3.20 1.20 4.30 3.00 3.00 3.00

2.7t

2.7t

11.4

t

11.4

t

6.8t

6.8t

6.8t

6.8t

1.10

1.80

3.20 1.20 4.30 3.00 3.00 3.00

clauses 207.1.3&207.4

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

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

11.4 250 5006.8 200 3802.7 150 200

Assuming 0.3m allowance for guide posts 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 0.45m

0.45m

3.25m

3.70m

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 7.25KN/m2 on left side is (f) =

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

6800

1200

4300

11.4t

11.4t

6.8t

1800

450

2750 3250

Area to be loadedwith 5KN/m² liveload + 2.25KN/m²silt load

Y

X

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

1.Wheel loads----Point loads 296.00KN

2.Live load in remaing portion(Left side)----UDL 22.185KN

2.Live load in remaing portion(Right side)----UDL 160.225KN

478.41KN

Resultant live load:-

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

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

S.No Distance from Y-axis Moment

1 57 0.70m 39.90KNm

2 57 0.70m 39.90KNm

3 57 2.50m 142.50KNm

4 57 2.50m 142.50KNm

5 34 0.64m 21.76KNm

6 34 2.44m 82.96KNm

7 22.185 0.225m 4.99KNm

8 160.225 4.375m 700.98KNm

478.410 1175.50KNm

Distance of centroid of forces from y-axis

= 2.457m


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 34 0.925m 31.45KNm

Wheel Load/UDL in KN

2 34 0.925m 31.45KNm

5 57 5.225m 297.83KNm

6 57 5.225m 297.83KNm

7 57 6.425m 366.22KNm

8 57 6.425m 366.22KNm

9 22.19KN 3.400m 75.43KNm

10 160.23KN 3.400m 544.77KNm

478.41 2011.19KN

Distance of centroid of forces from x-axis

= 4.204m


Location of resultant is as shown below:-

Calculation of reactions on abutments:-

Y

X

6800

6000

804

542

182.64KN

295.77KN

Hence,the critical reaction is Ra = 295.77KN

The corrected reaction = 295.77KN

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 = 0.01m

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 0.352

Reaction due to loads Ra =

Reaction due to point loads = Rb =

300

535 516

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 0.176

For the remaining portion,impact need not be considered.

4.Wind load:-

The deck system is located at height of (RTL-LBL) 1.68m

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 = 1.755

Breadth of the deck system = 7.4

The effective area exposed to wind force =HeightxBreadth =

Hence,the wind force acting at centroid of the deck system = 3.86KN(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 = 18.00KN

The location of the wind force from the top of RCC strip footing = 4.16m

5.Water current force:-

a)Water current force on deck slab:-

3.65m/sec

201.24

(where the value of 'K' is 1.5 )

Force acting on centroid of deck slab = 3.80KN

Kg/m2.

Velocity of stream at top,when the flow approaches the top of deck slab = √2 x Vmean =

P = 52KV2 = Kg/m2.

Point of action of water current force from the top of RCC strip footing = 3.09m

b)Water current force on abutment:-

Water pressure is considered on square ended abutments as per clause 213.2 of

IRC:6---2000 is

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 = 3.38KN

Point of action of water current force from the top of RCC strip footing = 2.88m

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

47.84KN

The location of the tractive force from the top of RCC strip footing = 3.86m

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 = 6.48Cum

ii)Volume of top footing = 2.43Cum

iii)Volume of 2nd footing = 2.70Cum

iv)Volume of 3rd footing = 2.97Cum

v)Volume of 4th footing = 0.00Cum

14.58Cum

Reduction in self wieght = 145.80KN

8.Earth pressure :-

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

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

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

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

'2Sin(a+Q)

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

sin(a+b)

Sin(a+Q) = SIN[3.14*(76.06+30)/180] = 0.961Sin(a-q) = SIN[3.14*(76.06-15)/180] = 0.875Sina = SIN[3.14*(76.06)/180] = 0.97Sin(Q+q) = SIN[3.14*(30+15)/180] = 0.707Sin(Q-b) = SIN[3.14*(30-0)/180] = 0.5Sin(a+b) = SIN[3.14*(76.06+0)/180] = 0.97

From the above expression,

0.3

The hieght of abutment above GL,as per the preliminary section assumed = 1.200m

Hence,maximum pressure at the base of the wall Pa = 6.48KN/sqm

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

Surcharge load = 6.48 KN/sqm

6.48

1.200

6.48 6.48

Ka =

Ka =

Area of the rectangular portion = 7.78Area of the triangular portion = 3.89

11.67

Taking moments of the areas about the toe of the wall

S.No Description Area Lever arm Moment

1 Rectangular 7.78 0.6 4.6682 Triangular 3.89 0.4 1.556

11.67 6.224

Height from the bottom of the wall = 0.53m

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

0.70

151.200m

0.53m

90

1.050

Total earth pressure acting on the abutment P = 69.98KN

67.60KN

18.10KN

Eccentricity of vertical component of earth pressure = 0.53m

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:-

As per clause 7.11.2.2(b) of IRC SP82:2007,the pressure due to static head will be zero at the surface of

water and will increase linearly to P = wh at depth 'h' from the surface, below which it will be constant as indicated

in the sketch below :-

Where, w = unit weight of water

h = afflux or depth of superstructure (including wearing coat) whichever is more.

Horizontal component of the earth pressure Ph =

Vertical component of the earth pressure Pv =

555 5.55KN/m²

1125

Total horizontal water pressure force = 11.48KN

The above pressure acts at height of 0.42H = 0.71m

11.Pressure due to eddies :-

2gWhere,

V = velocity of approach(w = unit weight of water; g= Acceleration due to gravity)

Pressure force due to eddies = 0.007KN

which is negligible.Hence it need not be considered

12. Pressure due to friction of water against piers and bottom of slab :-

Where,

ρ = mass density of water (w/g)

C = value of constant generally taken as10%

i)Force due to friction on Deck slab:-

Frictional force on bottom and top of deck slab = 4.96KN

The location of the frictional force from the top of RCC strip footing = 3.09m

ii)Force due to friction on abutment:-

Frictional force on the canal side face of abutment = 0.50KN

The location of the frictional force from the top of RCC strip footing = 1.50m

13. Force due to uplift under superstructure :-

This force acts vertically upwards and is given by

Pressure due to eddies = w (Vv-V)2

Vv = velocity of flow through the vents,

Pressure due to friction =f x ρ x (Cx Vv)2

f = friction coefficient = 1

Vv = velocity of flow through the vents (m/sec)

Uplift force = wh x Asp

555 5.55KN/m²

1125

Where,

h = the uplift head under the deckslab which may be taken as higher of the following two values: (i) Afllux(ii) Thickness of superstructure including wearing coat-head loss due to increase in

following expression

2g

Where,

V = velocity of approach

Afflux = 0.131m

Head loss due to increase in velocity = 0.012m

Hence,up lift head = 0.543m

Hence uplift force on the deck slab = 195.48KN

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 Strip 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

S.No Type of load

1 Reaction due to dead load from super structure 338.55KN 0.00 0.00

2 Self wieght of abutment&footings 349.92KN 0.015 0.000

3 347.83KN -0.01 0.543

4 Impact load 52.06 -0.01 0.543

1088.35

S.No Type of load Direction x or y

1 Wind load 18.00KN x-Direction 4.16

2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction 3.86

Asp area of the superstructure in plan

velocity through vents (Vv) Head loss due to increase in velocity through the vents is calculated by

h1 = Vv2-V2

Vv =velocity of flow through the vents

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

Intensity in KN

Eccentricty about x-axis(m)

Eccentricty about y-axis(m)

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

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

Intensity in KN

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

3 Water current force 3.38KN x-Direction 2.88

Check for stresses:-

About x-axis:-

Breadth of 3rd footing b = 6.00m

Depth of 3rd footing d = 1.65m

Area of the footing = A = 9.9

Section modulus of bottom footing 2.72

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 338.55KN 0.00 34.22 Self wieght of abutment&footings 349.92KN 0.02 35.883 Reaction due to live load with impact factor 347.83KN -0.01 34.784 Impact load 52.06KN -0.01 0

Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.86 -67.83

(Stress = -31.36*4.93/6.38)37.03

S.No Type of load Eccentricity

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 34.22 Self wieght of abutment&footings 349.92KN -0.02 34.823 Reaction due to live load with impact factor 347.83KN 0.01 35.494 Impact load 52.06KN -0.01 0

Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.86 67.83

172.34

Stress at heel = P/A(1+6e/b)+M/Z = 37.03 KN/Sqm>-2800KN/sqm.

Hence safe.

Stress at toe = P/A(1+6e/b)+M/Z = 172.34 KN/Sqm<5000KN/sqm

Hence safe.

About y-axis:-

m2

(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

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

Intensity in KN (P)

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

Breadth of 3rd footing b = 1.65m

Depth of 3rd footing d = 6.00m


Section modulus of bottom footing about = 9.90

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 338.55KN 0.00 34.22 Self wieght of abutment&footings 349.92KN 0.00 35.353 Reaction due to live load with impact factor 347.83KN -0.543 -34.244 Impact load 52.06KN 0.54 15.64

Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 4.16 -7.566 Water current force 3.38KN 2.88 -0.98

42.41

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 34.22 Self wieght of abutment&footings 349.92KN 0.00 35.353 Reaction due to live load with impact factor 347.83KN 0.543 104.514 Impact load 52.06KN 0.54 15.64

Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 4.16 7.566 Water current force 3.38KN 2.88 0.98

198.24

Stress at up stream side P/A(1+6e/b)+M/Z = 42.41 KN/Sqm>-2800KN/sqm.edge =

Hence safe.

Stress at down stream side P/A(1+6e/b)+M/Z = 198.24 KN/Sqm<5000KN/sqmedge =

Hence safe.

ii)On top of 3rd footing


m2

(1/6)bd2 = m3



Intensity in KN (P)


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

Intensity in KN (P)


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



S.No Type of load


2 Self wieght of abutment&footings 278.64KN 0.100 0.000

3 Reaction due to live load with impact factor 347.83KN -0.01 0.543

4 Impact load 52.06 -0.01 0.543






About x-axis:-

Breadth of 2nd footing b = 6.00mDepth of 2nd footing d = 1.50mArea of the footing = A = 9

Section modulus of Ist footing about 2.25

x-axis--Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



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

Intensity in KN



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

Intensity in KN


m2

(1/6)bd2 = m3



Intensity in KN (P)



34.24




180.21


Hence safe.


Hence safe.

About y-axis:-

Breadth of 1st footing b = 1.50mDepth of 1st footing d = 6.00mArea of the footing = A = 9


y-axis--Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



32.95

S.No Type of load

Intensity in KN (P)


m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)





218.21

Stress at up stream side P/A(1+6e/b)+M/Z = 32.95 KN/Sqm>-2800KN/sqm.edge =

Hence safe.

Stress at down stream side P/A(1+6e/b)+M/Z = 218.21 KN/Sqm<5000KN/sqmedge =

Hence safe.

i)On top of 2nd footing




S.No Type of load


2 Self wieght of abutment&cut waters 213.84KN 0.055 0.000


4 Impact load 52.06 -0.01 0.543






About x-axis:-


Intensity in KN




Intensity in KN


Breadth of 1st footing b = 6.00mDepth of 1st footing d = 1.35mArea of the footing = A = 8.1

Section modulus of base of abutment 1.82

about x-axis--Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



26.21




195.7


Hence safe.


Hence safe.

About y-axis:-



m2

(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



20.59

S.No Type of load



245.57

Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 20.59 KN/Sqm>-2800KN/sqm.

Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 245.57 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



Intensity in KN (P)



Intensity in KN (P)




S.No Type of load

1 Reaction due to dead load from super structure 338.55KN 0.00 0.002 Self wieght of abutment&footings 155.52KN 0.075 0.0003 Reaction due to live load with impact factor 347.83KN -0.01 0.543

4 Impact load 52.06 -0.01 0.543


1 Wind load 18.00KN x-Direction 3.562 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction 2.963 Water current force 3.38KN x-Direction 2.28


About x-axis:-

Breadth of abutment b = 6.00mDepth of abutment d = 1.05mArea of the footing = A = 6.3


about x-axis--Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



6.41


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 53.742 Self wieght of abutment&footings 155.52KN -0.07 22.833 Reaction due to live load with impact factor 347.83KN 0.01 55.76

Intensity in KN




Intensity in KN


m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)


4 Impact load 52.06KN -0.01 0Horizontal loads:- (Stress = M/Z)

5 Tractive,Braking&Frictional resistance of bearings 47.84KN 2.96 128.44

260.77


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 338.55KN 0.00 53.742 Self wieght of abutment&footings 155.52KN 0.00 24.693 Reaction due to live load with impact factor 347.83KN -0.543 25.234 Impact load 52.06KN 0.54 33.9


126.17

S.No Type of load


Horizontal loads:- (Stress = M/Z)

m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)



5 Wind load 18.00KN 3.56 10.176 Water current force 3.38KN 2.28 1.22

350.24



Hence safe.

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





S.No Type of load

1 Reaction due to dead load from super structure 338.55KNDeduct uplift pressure -195.48KNNet reaction due to dead load from super structure 143.07KN 0.00 0.00

Self wieght of abutment&cut waters 349.92KN

Reduction in self weight due to buoyancy -145.80KN

2 Net self weight 204.12KN 0.015 0.000

3 Vertical component of earth pressure 18.10KN 0.525 0.000




3 Water current force on deck slab 3.80KN x-Direction 3.09

4 Water current force on abutment 3.38KN x-Direction 2.88

5 Frictional force due to water on deck slab 4.96KN x-Direction 3.09

6 Frictional force due to water on abutment 0.50KN x-Direction 1.50

7 Horizontal load due to earth pressure 67.60KN y-Direction 1.43

8 Water pressure force 11.48KN y-Direction 1.61


Intensity in KN




Intensity in KN



About x-axis:-

Breadth of bottom footing b = 6.00mDepth of bottom footing d = 1.65mArea of the footing = A = 9.9


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 143.07KN 0.00 14.452 Net self wieght of abutment&footings 204.12KN 0.015 20.933 Vertical component of Earth pressure 18.10KN 0.53 2.79

Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 1.43 -35.595 Water pressure force 11.48KN 1.61 6.8

9.34999999999999


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 14.452 Net self wieght of abutment&footings 204.12KN -0.02 20.313 Vertical component of Earth pressure 18.10KN -0.53 0.87

Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 1.43 35.595 Water pressure force 11.48KN 1.61 -6.8

64.45


Hence safe.


Hence safe.

About y-axis:-


m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)


m2


about y-axis --Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load


Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 4.16 -7.565 Water current force on abutment 3.38KN 2.88 -1.06 Water current force on deck slab 3.80KN 3.09 -1.27 Frictional force due to water on deck slab 4.96KN 3.09 -1.68 Frictional force due to water on abutment 0.50KN 1.50 -0.1

25.54



Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 4.16 7.565 Water current force on abutment 3.38KN 2.88 1.06 Water current force on deck slab 3.80KN 3.09 1.27 Frictional force due to water on deck slab 4.96KN 3.09 1.68 Frictional force due to water on abutment 0.50KN 1.50 0.1

48.26



Hence safe.



(1/6)bd2 = m3



Intensity in KN (P)


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

Intensity in KN (P)




S.No Type of load


Self wieght of abutment&footings 278.64KN














About x-axis:-

Breadth of 2nd footing b = 6.00mDepth of 2nd footing d = 1.50mArea of the footing = A = 9


about x-axis --Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm


Intensity in KN




Intensity in KN


m2

(1/6)bd2 = m3



S.No Type of load



11.45




60.5


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 143.07KN 0.00 15.92 Net self wieght of abutment&footings 162.54KN 0.00 18.06

Intensity in KN (P)



Intensity in KN (P)


m2

(1/6)bd2 = m3



Intensity in KN (P)



3 Vertical component of Earth pressure 18.10KN 0.00 2.01Horizontal loads:- (Stress = M/Z)

4 Wind load 18.00KN 3.86 -7.725 Water current force on deck slab 3.80KN 2.79 -1.26 Water current force on abutment 3.38KN 2.58 -1.07 Frictional force due to water on deck slab 4.96KN 2.79 -1.58 Frictional force due to water on abutment 0.50KN 1.20 -0.1

24.49



Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.86 7.725 Water current force on deck slab 3.80KN 2.79 1.26 Water current force on abutment 3.38KN 2.58 1.07 Frictional force due to water on deck slab 4.96KN 2.79 1.58 Frictional force due to water on abutment 0.50KN 1.20 0.1

47.45



Hence safe.

iii)On top of 2nd footing




S.No Type of load


Self wieght of abutment&cut waters 213.84KN




Intensity in KN (P)



Intensity in KN













About x-axis:-



about x-axis --Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



12.74




Intensity in KN


m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)



57.85


Hence safe.


Hence safe.

About y-axis:-



about y-axis --Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load


Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.56 -7.915 Water current force on deck slab 3.80KN 2.49 -1.26 Water current force on abutment 3.38KN 2.28 -1.07 Frictional force due to water on deck slab 4.96KN 2.49 -1.58 Frictional force due to water on abutment 0.50KN 0.90 -0.1

23.68



Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.56 7.915 Water current force on deck slab 3.80KN 2.49 1.2

m2

(1/6)bd2 = m3



Intensity in KN (P)



Intensity in KN (P)


6 Water current force on abutment 3.38KN 2.28 1.07 Frictional force due to water on deck slab 4.96KN 2.49 1.58 Frictional force due to water on abutment 0.50KN 0.90 0.1

46.9



Hence safe.

iii)On top of 1st footing



S.No Type of load

1 Reaction due to dead load from super structure 338.55KNDeduct uplift pressure -195.48KNNet reaction due to dead load from super structure 143.07KN 0.00 0.00Self wieght of abutment&cut waters 213.84KNReduction in self weight due to buoyancy -89.10KN

2 Net self weight 124.74KN 0.055 0.0003 Vertical component of earth pressure 18.10KN 0.525 0.000


1 Wind load 18.00KN x-Direction 3.262 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.003 Water current force on deck slab 3.80KN x-Direction 2.194 Water current force on abutment 3.38KN x-Direction 1.985 Frictional force due to water on deck slab 4.96KN x-Direction 2.196 Frictional force due to water on abutment 0.50KN x-Direction 0.607 Horizontal load due to earth pressure 67.60KN y-Direction 0.538 Water pressure force 11.48KN y-Direction 0.71


About x-axis:-




Intensity in KN




Intensity in KN


m2

(1/6)bd2 = m3

about x-axis --Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load



22.63




68.13


Hence safe.


Hence safe.

About y-axis:-



about y-axis --Zy =

i.e, 5000KN/sqm



Intensity in KN (P)



Intensity in KN (P)


m2

(1/6)bd2 = m3



i.e, -2800KN/sqm

S.No Type of load


Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.26 -9.315 Water current force on deck slab 3.80KN 2.19 -1.36 Water current force on abutment 3.38KN 1.98 -1.17 Frictional force due to water on deck slab 4.96KN 2.19 -1.78 Frictional force due to water on abutment 0.50KN 0.60 -0.1

31.92



Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.26 9.315 Water current force on deck slab 3.80KN 2.19 1.36 Water current force on abutment 3.38KN 1.98 1.17 Frictional force due to water on deck slab 4.96KN 2.19 1.78 Frictional force due to water on abutment 0.50KN 0.60 0.1

58.84



Hence safe.

V)Check for stability of abutments:-

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




S.No Type of load

Intensity in KN (P)



Intensity in KN (P)



Intensity in KN




2 Self wieght of abutments 155.52KN 0.075 0.000


4 Vertical component of Active Earth pressure 18.10KN 0.525 0.00

912.05KN




3 Horizontal Active Earth pressure force 67.60KN y-Direction 0.53

133.44KN

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 = 141.61Kn-m

Moment due to active earth pressure force = 36.05Kn-m

Total overturning moment = 177.66Kn-m

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

Moment due to dead load reaction from super structure = 177.74Kn-m

Moment due to self weight of abutment = 93.31Kn-m

Moment due to live load reaction on abutment = 205.94Kn-m

Moment due to vertical component of active earth pressure = 19.01Kn-m

Total Restoring moment = 496.00Kn-m

Factor of safety = 2.79181252 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)

Check for stability against sliding:-

912.05KN


Intensity in KN


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

133.44KN

Coefficient of friction between concrete surfaces = 0.80

5.46799594 > 1.5 Hence safe

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

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




S.No Type of load


Self wieght of abutments 155.52KN

-64.80KN

2 Net self wieght 90.72KN 0.075 0.000

3 Vertical component of Active Earth pressure 18.10 0.525 0.00




3 Active Earth pressure force 67.60KN y-Direction 0.53

4 Force due to water pressure 11.48KN y-Direction 0.71



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

Moment due to active earth pressure force = 36.05Kn-m

Total overturning moment = 36.05Kn-m

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

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

Factor of safety against sliding Fs =


Intensity in KN



Reduction in self weight due to buoyancy


Intensity in KN


Moment due to dead load reaction from super structure = 75.11

Moment due to self weight of abutment = 54.43Kn-m

Moment due to water pressure force on the abutment = 8.10Kn-m

Moment due to vertical component of active earth pressure = 19.01Kn-m

Total Restoring moment = 156.65Kn-m



251.89KN

67.60KN

Coefficient of friction between concrete surfaces = 0.80

2.98107738 > 1.5 Hence safe


VI)Design of Strip footing:-

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

i)At the bottom of RCC strip footing




S.No Type of load


2 Self weight of abutment&footings 349.92KN 0.015 0.000

3 138.21KN 0.00 0.00

4 Reaction due to live load with impact factor 295.77KN 0.00 0.543


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

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



Intensity in KN



Self weight of RCC strip footing





Safe bearing capacity SBC of the soil = 15.00t/sqm


About x-axis:-

Breadth of footing b = 6.30m

Depth of footing d = 1.95m



about x-axis --Zx =

For RCC Strip footing permissible bearing pressure is 1.5xSBC = 225KN/sqm

No tension is allowed on soil as per clause 706.3.3.1 of IRC 78:2000

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 27.562 Self wieght of abutment&footings 349.92KN 0.02 28.893 Self weight of RCC strip footing 138.21KN 0.00 11.254 Reaction due to live load with impact factor 295.77KN 0.00 24.08

5 Vertical component of Earth pressure 18.10KN 0.53 2.21Horizontal loads:- (Stress = M/Z)

1 Wind load 18.00KN 0.00 02 Tractive,Braking&Frictional resistance of bearings 47.84KN 4.16 -49.93 Horizontal load due to earth pressure 67.60KN 1.73 -29.4

14.79


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 27.562 Self wieght of abutment&footings 349.92KN -0.02 28.083 Self weight of RCC strip footing 138.21KN 0.00 11.254 Reaction due to live load with impact factor 295.77KN 0.00 24.08

5 Vertical component of Earth pressure 18.10KN -0.53 0.74Horizontal loads:- (Stress = M/Z)


Intensity in KN


m2

(1/6)bd2 = m3

Intensity in KN (P)



Intensity in KN (P)


1 Wind load 18.00KN 0.00 02 Tractive,Braking&Frictional resistance of bearings 47.84KN 4.16 49.853 Horizontal load due to earth pressure 67.60KN 1.73 29.35

170.91

Stress at heel = P/A(1+6e/b)+M/Z = 14.79 KN/Sqm>0

Hence safe.


Hence safe.

About y-axis:-

Breadth of footing b = 1.95mDepth of footing d = 6.30mArea of the footing = A = 12.285


about y-axis --Zy =



S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 27.562 Self wieght of abutment&footings 349.92KN 0.00 28.483 Self weight of RCC strip footing 138.21KN 0.00 11.254 Reaction due to live load with impact factor 295.77KN -0.543 -16.155 Vertical component of Earth pressure 18.10KN 0.00 1.47

Horizontal loads:- (Stress = M/Z)1 Wind load 18.00KN 4.46 -6.222 Tractive,Braking&Frictional resistance of bearings 47.84KN 0.00 0.03 Horizontal load due to earth pressure 67.60KN 0.00 0.0

46.39


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 27.562 Self wieght of abutment&footings 349.92KN 0.00 28.483 Self weight of RCC strip footing 138.21KN 0.00 11.254 Reaction due to live load with impact factor 295.77KN 0.543 64.35 Vertical component of Earth pressure 18.10KN 0.00 1.47

Horizontal loads:- (Stress = M/Z)1 Wind load 18.00KN 4.46 6.222 Tractive,Braking&Frictional resistance of bearings 47.84KN 0.00 03 Horizontal load due to earth pressure 67.60KN 0.00 0

139.28

m2

(1/6)bd2 = m3

Intensity in KN (P)


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

Intensity in KN (P)


Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 46.39 KN/Sqm>0


Hence safe.

The footing has to be designed as strip footing supporting the masonry structure

The net bearing pressure on the toe of footing = 159.66 KN/Sqm(Excluding self weight of footing)

The footing needs to be designed for 1.5 times the above net bearing pressure 239.49 KN/Sqm

The UDL on the footing for unit width = 239.49 KN/m

The critical section for bending is at a distance of 1/4xwidth of bottom footing from the centre,ie,at section X--X

Hence,the length of cantilever portion to be considered for design =

0.83m

82.49KN-m

Effective depth required d = 157.51mm

The over all depth required(Assuming 16mm dia bars) = 215.51mm

However provide overall depth of = 450.00mm

Hence,effective depth = 392.00mm

Hence,the critical bending moment = (1/2)Wl2 =

Mu/0.133fckb =

b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4

X

Y

Y

d3d3

Bottom steel:-

0.537

From table 3 of SP 16,percentage of steel required = 0.156

Area of steel required = 611.52sqmm

Hence provide 12mm dia bars at 125mm c/c along width,the area of reinforcement comes to

904.32sqmmDistribution steel:-

Provide distribution reinforcement of 0.15% of cross sectional area of footing

Hence,the distribution reinforcement required = 675.00sqmm

Adopting 12mm dia bars,the spacing required = 167.00mm

However provide 12mm dia bars at 150mm c/c spacing,as distribution reinforcement

Check for one way shear:-

The critical section for beam shear is at distance of 'd' from the face of the column,ie,at Y-Y

35.92KN

0.1N/sqmm <2.8 N/sqmm(As per Table 20 of 1S 456)

Hence,the section is safe from shear point of view

Assumed percentage area of the steel reinforcement = 0.23%

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

0.35 137.20KN

0.35>0.1

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

The check for two way shear is not necessary in the present context.

Mu/bd2 =

Hence,the factored design shear force VFd =

Nominal shear stress Tv =

Hence Vuc =

Design of pier for bridge

I)Design Parameters:-

Clear Right Span = 6.00m

= 6.800m

Width of the carriage way = 6.00m

Thickness of deck slab as per IRC SP 20 = 0.480m

= 0.075m

Height of guard stones = 0.750m

Thickness of pier bed block = 0.30m

Sectional area of pier bed block = 0.410sqm

Thickness of strip footing = 0.45m

Height of pier = 1.200m

(As per hydralic calculations)

Top width of pier = 0.900m

Bottom width of pier = 0.90m

Sectional area of pier section = 1.080sqm

One side batter of pier = 0.000m

Other side batter of pier = 0.000m

Width of 1st footing = 1.20m

Thickness of 1st footing = 0.30m

One side offset of 1st footing wrt pier = 0.15m

Other side offset of 1st footing wrt pier = 0.15m

= 1.50m

= 0.30m

One side offset of 2nd footing wrt pier = 0.30m

Other side offset of 2nd footing wrt pier = 0.30m

Width of 3rd footing = 1.80m

Thickness of 3rd footing = 0.30m

One side offset of 3rd footing wrt pier = 0.45m

Other side offset of 3rd footing wrt pier = 0.45m

Width of VRCC strip footing = 2.40m

Deck slab length

Thickness of wearing coat

Width of 2nd footing

Thickness of 2nd footing

= 0.45m

= 0.75m

= 0.75m

Offset of top footing along width = 0.00m

Offset of 2nd footing along width = 0.00m

Offset of 3rd footing along width = 0.00m

= 0.15m

Type of bearings = No bearings proposed

= 25KN/cum

= 24KN/cum

= 5.645m

= 3.965m

= 6.235m

= 2.315m

= 15.00t/sqm

= 20.00N/sqmm

= 25.00N/sqmm

= 415.00N/sqmm

Cover to reinforcement = 50.00mm

= 10KN/cum

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.Seismic force9.Water pressure force

Apart from the above forces,the following pressures are to be considered as per clause 7.11.2.2 of IRC SP:82---2007:-

(a) Pressure due to static head due to afflux on upstream side and trough of

Thickness of VRCC strip footing (d3)

Canal side offset of RCC strip footing wrt pier (s5)

Bank side offset of RCC strip footing wrt pier (s6)

Offset of RCC strip footing along width (w1)

Unit weight of RCC (yrc)

Unit weight of PCC (ypc)

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 PCC (fck)

Compressive strength of concrete for VRCC Strip footing (fck)

Yield strength of steel (fy)

Unit weight of water (w)

standing wave on down stream side:

(b) Pressure due to velocity head

(c) Pressure due to eddies

(d) Pressure due to friction of water against piers and bottom of slab

(e) Force due to uplift under superstructure

super structure should also be considered:

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 pier:-

1.Dead Load:-

i)Self wieght of the deck slab = 489.60KN

ii)Self wieght of bed block over pier = 61.50KN

iii)Self weight of wearing coat = 76.50KN

627.60KN

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

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

iv)Self wieght of the pier section = 155.52KN

v)Self wieght of top footing = 51.84KN

vi)Self wieght of 2nd footing = 64.80KN

vii)Self wieght of 3rd footing = 77.76KN

As per the clause 7.11.3.4 of IRC:SP82--2007,Additional load of 150 mm thick silt with density equal to 15 kN/m 3 spread over the entire soffit(in case of box girders) and deck slabs of all types of

viii)Self wieght of 4th footing = 0.00KN

349.92KN

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

S.No Description Load in KN Distance of centroid of load from toe of pier

1 0 0.9

2 155.52 0.45

3 0 0

155.52

Location of resultant from toe of pier = 0.45m

Eccentricity wrt centre of base of pier = 0.000m

Back batter(W1)

Centre portion(W2)

Front batter(W3)

W1

W2

W3

b1

b2 b1 b3

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

S.No Description Load in KN

1 Back batter 0 1.05

2 Centre portion 155.52 0.6

3 Front batter 0 0.15

4 1st footing 51.84 0.6

207.36


Eccentricity wrt centre of 1st footing= 0.000m

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


1 Back batter 0 1.2

2 Centre portion 155.52 0.75

3 Front batter 0 0.3

4 1st footing 51.84 0.75

Distance of centroid of load from toe of 1st footing

Distance of centroid of load from toe of 2nd footing

5 2nd footing 64.8 0.75

272.16



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


1 Back batter 0 1.352 Centre portion 155.52 0.93 Front batter 0 0.454 1st footing 51.84 0.905 2nd footing 64.8 0.906 3rd footing 77.76 0.90

349.92



2.Live Load:-

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

GENERAL IRC Class-A loading Pattern

Distance of centroid of load from toe of 3rd footing

are to be designed for IRC Class A loading.

2.7t

2.7t

11.4

t

11.4

t

6.8t

6.8t

6.8t

6.8t

1.10

1.80

3.20 1.20 4.30 3.00 3.00 3.00

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)

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

2.7t

2.7t

11.4

t

11.4

t

6.8t

6.8t

6.8t

6.8t

1.10

1.80

3.20 1.20 4.30 3.00 3.00 3.00

Y

X

6800

1200

4300

11.4t

11.4t

6.8t

1800

450

2750 3250


11.4 250 5006.8 200 3802.7 150 200

Assuming 0.3m allowance for guide posts 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 0.45m

0.45m

3.25m

3.70m

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 0.70m

2 57 0.70m

3 57 2.50m

4 57 2.50m

Hence,the width of area to be loaded with 7.25KN/m2 on left side is (f) =

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

Wheel Load/UDL in KN

5 34 0.64m

6 34 2.44m

7 22.185 0.225m

8 160.225 4.375m

478.410

Distance of centroid of forces from y-axis

= 2.457m


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 34 0.925m

2 34 0.925m

5 57 5.225m

6 57 5.225m

7 57 6.425m

8 57 6.425m

9 22.19KN 3.400m

10 160.23KN 3.400m

478.41

Distance of centroid of forces from x-axis

= 4.204m


Calculation of reactions on pier:-

421.85KN

56.56KN

Hence,the critical reaction is Ra = 421.8KN

The corrected reaction = 421.85KN

Reaction due to point loads Ra =

Reaction due to point loads = Rb =

Y

X

6800

2750 3250

804

543

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

The eccentricty of the line of action of live load = 0.00m

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)

220220

460

900

1200

Hence,the factor is 0.352

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 pier will be

For the remaining portion,impact need not be considered.

4.Wind load:-

The deck system is located at height of (RTL-LBL) 1.68m

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 = 1.755

Breadth of the deck system = 7.4

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 strip footing =

5.Water current force:-

a)Water current force on deck slab:-

Kg/m2.

284.7

(where the value of 'K' is 1.5 )

Force acting on centroid of deck slab = 10.74KN

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

b)Water current force on pier:-

Water pressure is considered on square ended piers as per clause 213.2 of

IRC:6---2000 is

Hence,the water current force = 4.30KN

Point of action of water current force from the top of RCC strip 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 pier is

47.84KN

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

Velocity of stream at top,when the flow approaches the top of deck slab = √2 x Vmean =

P = 52KV2 = Kg/m2.

7.Buoyancy :-

As per clause 216.4 of IRC:6---2000,for abutments or piers of shallow depth,the dead weight of the pier 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 pier is scoured.

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

i)Volume of pier section = 6.48Cum

ii)Volume of top footing = 2.16Cum

iii)Volume of 2nd footing = 2.70Cum

iv)Volume of 3rd footing = 3.24Cum

v)Volume of 4th footing = 0.00Cum

14.58Cum

Reduction in self wieght = 145.80KN

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:-



in the sketch below :-

Where, w = unit weight of water

h = afflux or depth of superstructure (including wearing coat) whichever is more.

555 5.55KN/m²

1125

Total horizontal water pressure force = 16.09KN

The above pressure acts at height of 0.42H = 0.71m

11.Pressure due to eddies :-

2gWhere,

V = velocity of approach(w = unit weight of water; g= Acceleration due to gravity)

Pressure force due to eddies = 0.014KN

which is negligible.Hence it need not be considered

12. Pressure due to friction of water against piers and bottom of slab :-

Where,

ρ = mass density of water (w/g)

C = value of constant generally taken as10%

Pressure due to eddies = w (Vv-V)2

Vv = velocity of flow through the vents,

Pressure due to friction =f x ρ x (Cx Vv)2

f = friction coefficient = 1

Vv = velocity of flow through the vents (m/sec)

555 5.55KN/m²

1125

i)Force due to friction on Deck slab:-

Frictional force on bottom and top of deck slab = 4.96KN

The location of the frictional force from the top of RCC strip footing =

ii)Force due to friction on pier:-

Frictional force on both faces of pier = 0.50KN

The location of the frictional force from the top of RCC strip footing =

13. Force due to uplift under superstructure :-

This force acts vertically upwards and is given by

Where,

h = the uplift head under the deckslab which may be taken as higher of the following two values: (i) Afllux(ii) Thickness of superstructure including wearing coat-head loss due to increase in

following expression

2g

Where,

V = velocity of approach

Afflux = 0.131m

Head loss due to increase in velocity = 0.012m

Hence,up lift head = 0.543m

Hence uplift force on the deck slab = 221.54KN

IV)Check for stresses for pier&footings:-

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



Uplift force = wh x Asp

Asp area of the superstructure in plan

velocity through vents (Vv) Head loss due to increase in velocity through the vents is calculated by

h1 = Vv2-V2

Vv =velocity of flow through the vents



S.No Type of load

1 Reaction due to dead load from super structure 627.60KN 0.00

2 Self wieght of pier&footings 349.92KN 0.000

3 421.85KN 0.00

4 Impact load 0.00 0.00

1399.37


1 Wind load 18.00KN x-Direction

2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction

3 Water current force 0.00KN x-Direction


About x-axis:-

Breadth of bottom footing b = 6.00m

Depth of bottom footing d = 1.80m



about x-axis --Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

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

Intensity in KN


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

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

Intensity in KN

m2

(1/6)bd2 = m3

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


S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Reaction due to live load with impact factor 421.85KN 0.004 Impact load 0.00KN 0.00

Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.86

(Stress = -31.36*4.93/6.38)




(Stress = 31.36*4.93/6.38)


Hence safe.


Hence safe.

About y-axis:-

Breadth of bottom footing b = 1.80m

Depth of bottom footing d = 6.00m


Section modulus of bottom footing about = 10.80

y-axis--Zy =

Intensity in KN (P)


Intensity in KN (P)

m2

(1/6)bd2 = m3


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 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Reaction due to live load with impact factor 421.85KN -0.5434 Impact load 0.00KN 0.00

Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 4.166 Water current force 0.00KN 0.00

S.No Type of load



Stress at up stream side P/A(1+6e/b)+M/Z = 101.43 KN/Sqm>-2800KN/sqm.edge of pier =

Hence safe.

Stress at down stream side P/A(1+6e/b)+M/Z = 157.71 KN/Sqm<5000KN/sqmedge of pier =

Hence safe.





Intensity in KN (P)


Intensity in KN (P)



S.No Type of load



3 Reaction due to live load with impact factor 421.85KN 0.00







About x-axis:-



x-axis--Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load

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

Intensity in KN


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

Intensity in KN

m2

(1/6)bd2 = m3



Intensity in KN (P)








Hence safe.


Hence safe.

About y-axis:-



y-axis--Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

Intensity in KN (P)

m2

(1/6)bd2 = m3



S.No Type of load


Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.866 Water current force 0.00KN -0.30

S.No Type of load



Stress at up stream side P/A(1+6e/b)+M/Z = 113.67 KN/Sqm>-2800KN/sqm.edge of pier =

Hence safe.

Stress at down stream side P/A(1+6e/b)+M/Z = 180.01 KN/Sqm<5000KN/sqmedge of pier =

Hence safe.

i)On top of 2nd footing




Intensity in KN (P)


Intensity in KN (P)



S.No Type of load










About x-axis:-

Breadth of pier b = 6.00mDepth of pier d = 1.20mArea of the footing = A = 7.2

Section modulus of base of pier 1.44

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 627.60KN 0.002 Self wieght of pier&footings 207.36KN 0.003 Reaction due to live load with impact factor 496.09KN 0.00

Intensity in KN



Intensity in KN

m2

(1/6)bd2 = m3



Intensity in KN (P)


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

5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.26





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



S.No Type of load



S.No Type of load



Stress at up stream side edge of pier = P/A(1+6e/b)+M/Z = 138.56 KN/Sqm>-2800KN/sqm.

Hence safe.Stress at down stream side edge of pier = P/A(1+6e/b)+M/Z = 231.18 KN/Sqm<5000KN/sqm

Hence safe.

i)On top of 1st footing



S.No Type of load

Intensity in KN (P)


Intensity in KN (P)



Intensity in KN


1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&cut waters 155.52KN 0.0003 Reaction due to live load with impact factor 421.85KN 0.00



1 Wind load 18.00KN x-Direction2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction3 Water current force 0.00KN x-Direction


About x-axis:-



about x-axis--Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load




Intensity in KN

m2

(1/6)bd2 = m3



Intensity in KN (P)






Hence safe.


Hence safe.

About y-axis:-



about y-axis--Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 155.52KN 0.003 Reaction due to live load with impact factor 421.85KN -0.543

Intensity in KN (P)

m2

(1/6)bd2 = m3



Intensity in KN (P)


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

5 Wind load 18.00KN 3.566 Water current force 0.00KN 0.00

S.No Type of load





Hence safe.

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





S.No Type of load

1 Reaction due to dead load from super structure 627.60KNDeduct uplift pressure -221.54KNNet Reaction due to dead load from super structure 406.06KN 0.00

Intensity in KN (P)



Intensity in KN


Self wieght of pier&cut waters 349.92KN


2 Net self weight 204.12KN 0.000




3 Water current force on deck slab 10.74KN x-Direction

4 Water current force on pier 4.30KN x-Direction

5 Frictional force due to water on deck slab 4.96KN x-Direction

6 Frictional force due to water on pier 0.50KN x-Direction

7 Water pressure force 16.09KN y-Direction


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 406.06KN 0.002 Net self wieght of pier&footings 204.12KN 0.003 Vertical component of Earth pressure 0.00KN 0.00


Intensity in KN

m2

(1/6)bd2 = m3



Intensity in KN (P)


Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 0.00KN 0.005 Water pressure force 16.09KN 1.61





Hence safe.


Hence safe.

About y-axis:-



about y-axis --Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load

Intensity in KN (P)

m2

(1/6)bd2 = m3



Intensity in KN (P)



Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 4.165 Water current force on deck slab 10.74KN 3.096 Water current force on pier 4.30KN 2.107 Frictional force due to water on deck slab 4.96KN 3.098 Frictional force due to water on pier 0.50KN 1.50






Hence safe.





Intensity in KN (P)


S.No Type of load


Self wieght of pier&cut waters 272.16KN



3 Vertical component of earth pressure 0.00KN 0.000








7 Horizontal load due to earth pressure 0.00KN y-Direction



About x-axis:-



about x-axis --Zx =

i.e, 5000KN/sqm

Intensity in KN



Intensity in KN

m2

(1/6)bd2 = m3



i.e, -2800KN/sqm

S.No Type of load







Hence safe.


Hence safe.

About y-axis:-



about y-axis --Zy =

i.e, 5000KN/sqm

Intensity in KN (P)


Intensity in KN (P)

m2

(1/6)bd2 = m3


i.e, -2800KN/sqm

S.No Type of load








Hence safe.

iii)On top of 2nd footing


Intensity in KN (P)


Intensity in KN (P)




S.No Type of load


Self wieght of pier&footings 207.36KN














About x-axis:-



Intensity in KN



Intensity in KN

m2


about x-axis --Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load







Hence safe.


Hence safe.

About y-axis:-

Breadth of pier b = 1.20m

(1/6)bd2 = m3



Intensity in KN (P)


Intensity in KN (P)

Depth of pier d = 6.00mArea of the footing = A = 7.2


about y-axis --Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load







m2

(1/6)bd2 = m3



Intensity in KN (P)


Intensity in KN (P)


Hence safe.

iii)On top of 1st footing



S.No Type of load

1 Reaction due to dead load from super structure 627.60KNDeduct uplift pressure -221.54KNNet Reaction due to dead load from super structure 406.06KN 0.00Self wieght of pier&footings 155.52KNReduction in self weight due to buoyancy -64.80KN

2 Net self weight 90.72KN 0.0003 Vertical component of earth pressure 0.00KN 0.000


1 Wind load 18.00KN x-Direction2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction3 Water current force on deck slab 10.74KN x-Direction4 Water current force on pier 4.30KN x-Direction5 Frictional force due to water on deck slab 4.96KN x-Direction6 Frictional force due to water on pier 0.50KN x-Direction7 Horizontal load due to earth pressure 0.00KN y-Direction8 Water pressure force 16.09KN y-Direction


About x-axis:-



Intensity in KN



Intensity in KN

m2


about x-axis --Zx =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load







Hence safe.


Hence safe.

About y-axis:-

Breadth of pier b = 0.90m

(1/6)bd2 = m3



Intensity in KN (P)


Intensity in KN (P)

Depth of pier d = 6.00mArea of the footing = A = 5.4


about y-axis --Zy =

i.e, 5000KN/sqm

i.e, -2800KN/sqm

S.No Type of load





Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 18.00KN 3.265 Water current force on deck slab 10.74KN 2.196 Water current force on pier 4.30KN 1.207 Frictional force due to water on deck slab 4.96KN 2.198 Frictional force due to water on pier 0.50KN 0.60


m2

(1/6)bd2 = m3



Intensity in KN (P)


Intensity in KN (P)


Hence safe.

V)Check for stability of pier:-





S.No Type of load


2 Self wieght of pier 155.52KN 0.000


4 Vertical component of Active Earth pressure 0.00KN 0.000

1204.97KN




3 Horizontal Active Earth pressure force 0.00KN y-Direction

65.84KN


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

Moment due to tractive,braking&frictional resistance of bearings =


Intensity in KN



Intensity in KN

Moment due to active earth pressure force =

Total overturning moment =

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

Moment due to dead load reaction from super structure =

Moment due to self weight of pier =

Moment due to live load reaction on pier =

Moment due to vertical component of active earth pressure =

Total Restoring moment =



Coefficient of friction between concrete surfaces =

14.6409083 > 1.5 Hence safe


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




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

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



S.No Type of load


Self wieght of pier 155.52KN

-64.80KN

2 Net self wieght 90.72KN 0.000

3 Vertical component of Active Earth pressure 0.00 0.000








7 Active Earth pressure force 0.00KN y-Direction

8 Force due to water pressure 16.09KN y-Direction



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 pier =

Intensity in KN


Reduction in self weight due to buoyancy


Intensity in KN

Moment due to water pressure force on the pier =

Moment due to vertical component of active earth pressure =

Total Restoring moment =

Factor of safety = ∞ > 2.0 Hence safe



Coefficient of friction between concrete surfaces =

∞ > 1.5 Hence safe


VI)Design of Strip footing:-


i)At the bottom of RCC strip footing




S.No Type of load


2 Self weight of pier&footings 349.92KN 0.000

3 170.10KN 0.00

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

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



Intensity in KN


Self weight of RCC strip footing







Safe bearing capacity SBC of the soil = 15.00t/sqm


About x-axis:-

Breadth of footing b = 6.30m

Depth of footing d = 2.40m



about x-axis --Zx =



S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Self weight of RCC strip footing 170.10KN 0.004 Reaction due to live load with impact factor 421.85KN 0.00

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

1 Wind load 18.00KN 0.002 Tractive,Braking&Frictional resistance of bearings 47.84KN 4.163 Horizontal load due to earth pressure 0.00KN 0.00


Intensity in KN

m2

(1/6)bd2 = m3

Intensity in KN (P)



Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Self weight of RCC strip footing 170.10KN 0.004 Reaction due to live load with impact factor 421.85KN 0.00

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

1 Wind load 18.00KN 0.002 Tractive,Braking&Frictional resistance of bearings 47.84KN 4.163 Horizontal load due to earth pressure 0.00KN 0.00

Stress at heel = P/A(1+6e/b)+M/Z = 70.89 KN/Sqm>0

Hence safe.


Hence safe.

About y-axis:-

Breadth of footing b = 2.40mDepth of footing d = 6.30mArea of the footing = A = 15.12


about y-axis --Zy =



S.No Type of load

Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Self weight of RCC strip footing 170.10KN 0.00

Intensity in KN (P)

m2

(1/6)bd2 = m3

Intensity in KN (P)


4 Reaction due to live load with impact factor 421.85KN -0.5435 Vertical component of Earth pressure 0.00KN 0.00

Horizontal loads:- (Stress = M/Z)1 Wind load 18.00KN 4.462 Tractive,Braking&Frictional resistance of bearings 47.84KN 0.003 Horizontal load due to earth pressure 0.00KN 0.00


Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Self weight of RCC strip footing 170.10KN 0.004 Reaction due to live load with impact factor 421.85KN 0.5435 Vertical component of Earth pressure 0.00KN 0.00

Horizontal loads:- (Stress = M/Z)1 Wind load 18.00KN 4.462 Tractive,Braking&Frictional resistance of bearings 47.84KN 0.003 Horizontal load due to earth pressure 0.00KN 0.00

Stress at up stream side edge of pier = P/A(1+6e/b)+M/Z = 60.87 KN/Sqm>0


Hence safe.

The footing has to be designed as strip footing supporting the masonry structure

The net bearing pressure on the toe of footing = 125.46 KN/Sqm(Excluding self weight of footing)

The footing needs to be designed for 1.5 times the above net bearing pressure 188.19 KN/Sqm

Intensity in KN (P)

b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4

X

Y

Y

d3d3

The UDL on the footing for unit width = 188.19 KN/m


Hence,the length of cantilever portion to be considered for design =

0.83m

64.82KN-m

Effective depth required d = 139.62mm

The over all depth required(Assuming 16mm dia bars) = 197.62mm

However provide overall depth of = 450.00mm

Hence,effective depth = 392.00mm

Bottom steel:-

0.422

From table 3 of SP 16,percentage of steel required = 0.127Minimum percentage required = 0.15

Area of steel required = 588.00sqmm

However provide 12mm dia bars at 125mm c/c along width,the area of reinforcement comes to

904.32sqmmDistribution steel:-

Hence,the critical bending moment = (1/2)Wl2 =

Mu/0.133fckb =

Mu/bd2 =

b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4

X

Y

Y

d3d3

Provide distribution reinforcement of 0.15% of cross sectional area of footing

Hence,the distribution reinforcement required = 675.00sqmm

Adopting 12mm dia bars,the spacing required = 167.00mm

However provide 12mm dia bars at 150mm c/c spacing,as distribution reinforcement

Check for one way shear:-


56.46KN

0.1N/sqmm <2.8 N/sqmm(As per Table 20 of 1S 456)

Hence,the section is safe from shear point of view

Assumed percentage area of the steel reinforcement = 0.23%

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

0.35 137.20KN

0.35>0.1


The check for two way shear is not necessary in the present context.

Hence,the factored design shear force VFd =

Nominal shear stress Tv =

Hence Vuc =

Design of pier for bridge

No bearings proposed

thick silt with density

Moment

0

69.98

0

69.98

W1

W2

W3

b1

b2 b1 b3

Moment

0

93.31

0

31.1

124.41

Moment

0

116.64

0

38.88

48.6

204.12

Moment

0139.97

046.6658.3269.98

314.93

2.7t

2.7t

11.4

t

11.4

t

6.8t

6.8t

6.8t

6.8t

1.10

1.80

3.20 1.20 4.30 3.00 3.00 3.00

is severe and the same is to be considered as per

2.7t

2.7t

11.4

t

11.4

t

6.8t

6.8t

6.8t

6.8t

1.10

1.80

3.20 1.20 4.30 3.00 3.00 3.00

Y

X

6800

1200

4300

11.4t

11.4t

6.8t

1800

450

2750 3250


296.00KN

22.19KN

160.23KN

478.41KN

Moment

39.90KNm

39.90KNm

142.50KNm

142.50KNm

21.76KNm

82.96KNm

4.99KNm

700.98KNm

1175.50KNm

Moment

31.45KNm

31.45KNm

297.83KNm

297.83KNm

366.22KNm

366.22KNm

75.43KNm

544.77KNm

2011.19KN

Y

X

6800

2750 3250

804

543

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

220220

460

900

1200

0.176

3.86KN

18.00KN

4.16m

3.65m/sec

3.09m

2.10m

3.86m



555 5.55KN/m²

1125

3.09m

1.50m

h = the uplift head under the deckslab which may be taken as higher of the following two values: (i) Afllux

) Head loss due to increase in velocity through the vents is calculated by

0.00

0.000

0.543

0.00

4.16

3.86

0.00



58.1132.4

39.060

-57

72.57

58.1132.4

39.060

57

186.57

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



58.1132.4

17.850

-6.930

101.43

58.1132.4

60.270

6.930

157.71

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



0.00

0.000

0.543

0.00

3.86

3.56

-0.30




69.7330.2446.87

0

-75.7

71.14

69.7330.2446.87

0

75.7

222.54

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm


69.7330.2421.42

0

-7.720

113.67

69.7330.2472.32

0

7.720

180.01

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



0.00

0.000

0.543

0.00

3.56

3.26

-0.60

87.1728.868.9


composes of the following components



0

-108.31

76.56

87.1728.868.9

0

108.31

293.18

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm


87.1728.8

31.490

-8.90

138.56

87.1728.8

106.310

8.90

231.18

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm




0.000.0000.543

0.00

3.562.960.00

116.2228.8

78.120

-174.83

48.31



116.2228.8

78.120

174.83

397.97

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm

116.2228.835.7



0

-11.870

168.85

116.2228.8

120.540

11.870

277.43

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm

0.00



0.000

4.16

0.00

3.09

2.10

3.09

1.50

1.61

37.618.9

0



08.0

64.47

37.618.9

0

0-8.0

48.53

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



37.618.9

0

-6.93-3.1-0.8-1.4-0.1

44.17

37.618.9

0

6.933.10.81.40.1

68.83

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm


0.00

0.000

0.000

3.86

0.00

2.79

1.80

2.79

1.20

0.00

1.31



45.1217.64

0

09.3

72.1

45.1217.64

0

0-9.3

53.42

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



45.1217.64

0

-7.72-3.3-0.9-1.5-0.1

49.24

45.1217.64

0

7.723.30.91.50.1

76.28

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



0.00

0.000

0.000

3.56

0.00

2.49

1.50

2.49

0.90

0.00

1.01



56.416.8

0

011.2

84.44

56.416.8

0

0-11.261.96

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



56.416.8

0

-8.9-3.7-0.9-1.7-0.1

57.91

56.416.8

0

8.93.70.91.70.1

88.49

KN/Sqm>-2800KN/sqm.



KN/Sqm<5000KN/sqm

0.00

0.0000.000

3.260.002.191.202.190.600.000.71



75.216.8

0

014.0

106.02

75.216.8

0

0-14.077.98

KN/Sqm>-2800KN/sqm.

KN/Sqm<5000KN/sqm



75.216.8

0

-10.87-4.4-1.0-2.0-0.1

73.74

75.216.8

0

10.874.41.02.00.1

110.26

KN/Sqm>-2800KN/sqm.



KN/Sqm<5000KN/sqm

0.00

0.000

0.543

0.00

3.26

2.96

0.00

141.61Kn-m


composes of the following components


0.00Kn-m

141.61Kn-m

282.42Kn-m

69.98Kn-m

189.83Kn-m

0.00Kn-m

542.23Kn-m


1204.97KN

65.84KN

0.80


0.00

0.000

0.00

3.26

0.00

2.19

1.20

2.19

0.60

0.00

0.71

0.00Kn-m

0.00Kn-m

0.00Kn-m

40.82Kn-m



11.35Kn-m

0.00Kn-m

52.18Kn-m


106.81KN

0.00KN

0.80


0.00

0.000

0.00


0.543

0.000

4.46

4.16

0.00

41.5123.1411.2527.9

0

0-32.90.0



70.89

41.5123.1411.2527.9

0

032.91

0136.71

KN/Sqm<225KN/sqm

41.5123.1411.25


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

-9.970

-5.060.00.0

60.87

41.5123.1411.2565.77

0

5.0600

146.73

KN/Sqm<225KN/sqm


b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4

X

Y

Y

d3d3


However provide 12mm dia bars at 125mm c/c along width,the area of reinforcement comes to

b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4

X

Y

Y

d3d3

DESIGN OF FACE WALL (BIT-I)

Data:-

Height of Retaining wall =Height of wall above G.L=Height of wall below G.L=Density of back fill soil&material in toe portion = Unit weight of concrete =Top width =Bottom width assumed =Ground water Table level =

(in clock wise direction)

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

Coefficient of active earth pressure by Coulomb's theory

Sin(a+Q)


sin(a+b)


0.57

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


Surcharge load = 615.6

615.6

2.40m

2462.40

Total earth pressure = 4432.32

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

0.30

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) =

Ka =

Ka =

46.53

2.40m

63.470.3 C

0.151.50

Stability calculations:-Load(Kg)

Weight of the wall = 1728.00Kg3456.00Kg

Weight of the earth = 2592.00KgVertical component of Active earth pressure= 3215.43KgWeight of soil on the heel of footing-I = 1296.00Kg

12287.43Kg

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

Horizontal earth pressure force = 3050.65

Lever arm x = M = 0.65mV

Eccentricuty e = b/2-x = 0.10m <b/6

Maximum stress = P/A(1+6e/b) = 11468.27 < SBC Hence O.K

Minimum stress = P/A(1-6e/b) = 4914.97 Hence O.K

Coefficient of friction between soil and footing u = 0.5

1.81 >1.25

Factor of safety against overturning = 3.27 >1.5



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

DESIGN OF FACE WALL (BIT-II)

Data:-

Height of Retaining 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 =Unit weight of concrete =Top width =Bottom width assumed =Ground water Table level =


Permissible compressive stress in bending for M20 Concrete (c)=Permissible tensile stress in bending for Fe 415 steel (t)=Modular ratio m = 280/3c =k = mc/(mc+t)j = 1-k/3 =R = 1/2(cjk) =Surcharge over the back fill in terms of height of back fill =Safe bearing capacity =


Sin(a+Q)


sin(a+b)


0.57




615.6

1.80m



Ka =

Ka =

1846.80



0.30

46.53

1.80m

63.470.3 C

0.151.20




7679.65Kg










1.81 >1.25


DESIGN OF FACE WALL (BIT-III)

Data:-





Sin(a+Q)


sin(a+b)


0.51







Ka =

Ka =

550.8

1.20m

1101.60



0.30

42.59

1.20m

67.410.3 C

0.150.80




3666.24Kg










1.69 >1.25


DESIGN OF FACE WALL (BIT-IV)

Data:-





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

sin(a+b)


0.42





Ka =

Ka =



453.6

0.80m

604.80



0.30

34

0.80m

760.3 C

0.150.50




1682.05Kg










1.51 >1.25



DESIGN OF FACE WALL (BIT-I)

2.40m2.40m0.00m

1800Kg/Cum2400Kg/Cum

0.30m1.50m

3063.47

020

0.60m15000.0Kg/Sqm

2

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

2462.40Kg/sqm

3050.65Kg/sqm

3215.43Kg/sqm

Lever arm about C Moment(Kg-m)

0.15 259.200.70 2419.201.10 2851.201.21 3875.931.65 2138.40

11543.93


1.16m -3532.658011.28

Hence O.K

Hence O.K

DESIGN OF FACE WALL (BIT-II)

1.80m1.80m0.00m

1800Kg/CumM15

Fe4152400Kg/Cum

0.30m1.20m

3063.47

02070Kg/Sqcm

2300Kg/Sqcm13

0.2830.9068.9740.60m

15000.0Kg/Sqm

2

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

1846.80Kg/sqm

1906.65Kg/sqm

2009.65Kg/sqm


0.15 194.400.60 1166.400.90 1312.200.90 1816.841.35 1312.20

5802.04


0.91m -1727.434074.61

Hence O.K

Hence O.K

DESIGN OF FACE WALL (BIT-III)

1.20m1.20m0.00m

1800Kg/CumM15

Fe4152400Kg/Cum

0.30m0.80m

3067.41

02070Kg/Sqcm

2300Kg/Sqcm13

0.2830.9068.9740.60m

15000.0Kg/Sqm

2

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

1101.60Kg/sqm

973.55Kg/sqm

894.24Kg/sqm


0.15 129.600.47 336.000.63 342.000.58 520.390.95 615.60

1943.59


0.65m -636.701306.89

Hence O.K

Hence O.K

DESIGN OF FACE WALL (BIT-IV)

0.80m0.80m0.00m

1800Kg/CumM15

Fe4152400Kg/Cum

0.30m0.50m

3076

02070Kg/Sqcm

2300Kg/Sqcm13

0.2830.9068.9740.60m

15000.0Kg/Sqm

2

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

604.80Kg/sqm

501.50Kg/sqm

338.05Kg/sqm


0.15 86.400.37 70.400.43 62.400.36 122.850.65 280.80

622.85


0.49m -243.73379.12

Hence O.K

Hence O.K

Hydraulic design

Hydraulic Particulars:-

1.Maximum Flood Level 6.235

2.Ordinary Flood level 5.015

3.Lowest Bed level 3.965

4.Average bed slope 0.015200(1 in 1000)

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

6.Bottom of deck proposed 5.165(MFL+Vertical clearence)

7.Road Crest level 5.645(Bottom of deck level+thickness of deck slab)

8.Width of carriage way 6.000

Discharge Calculations:-

I)Discharge calculations of stream:-

A) Area-Velocity Method:-

a)At the proposed bridge site(20m upstream):-

Maximum Flood level 6.235mSlope 0.01520Rugosity Coefficient 0.050

S.No Chainage R.L Depth of Average Distance Area Wetted flow depth of (m) (Sqm) perimeter(m) flow (m)

(m)

1 0 6.500 0.00 0.00 0.00 0.00 0.002 1 5.340 0.90 0.45 1.00 0.45 1.083 2 4.560 1.68 1.29 1.00 1.29 1.054 4 3.965 2.27 1.97 2.00 3.95 2.055 6 4.780 1.46 1.86 2.00 3.73 2.346 7 5.300 0.94 1.20 1.00 1.20 1.127 9 6.100 0.14 0.54 2.00 1.07 2.308 10 6.420 0.00 0.07 1.00 0.07 1.05

11.74 10.99

Hydraulic Radius R= Total area/Wetted perimeter = 1.07

Velocity V = 2.58m/sec

AXV 30.28Cumecs

5.Rugosity Coefficient(n)

1/nX(R2/3XS1/2)

Discharge =

b)At 300m upstream of the the proposed bridge site:-



(m)

1 0 9.450 0.00 0.00 0.00 0.00 0.002 1 8.290 0.95 0.47 1.00 0.47 1.083 2 7.720 1.51 1.23 1.00 1.23 1.054 4 7.500 1.73 1.62 2.00 3.25 2.055 6 7.650 1.58 1.66 2.00 3.32 2.346 8 8.250 0.98 1.28 2.00 2.57 2.207 10 9.050 0.18 0.58 2.00 1.17 2.308 13 9.370 0.00 0.09 3.00 0.28 3.20

12.29 14.22



AXV 27.41Cumecs

c)At 300m downstream of the the proposed bridge site:-



(m)

1 0 4.400 0.00 0.00 0.00 0.00 0.002 1 3.240 0.79 0.40 1.00 0.40 1.083 2 2.460 1.58 1.19 1.00 1.19 1.054 4 1.660 2.38 1.98 2.00 3.95 2.055 6 1.770 2.27 2.32 2.00 4.64 2.346 8 3.200 0.84 1.55 2.00 3.10 2.207 10 3.750 0.29 0.56 2.00 1.12 2.308 13 4.320 0.00 0.14 3.00 0.43 3.20

14.82 14.22



AXV 37.49Cumecs

1/nX(R2/3XS1/2)

Discharge =

1/nX(R2/3XS1/2)

Discharge =

B) CATCHMENT AREA METHOD:-

Catchment area from stream alignment and local enquiry(Indicated in the drawing) = 1.38sqkm

21.65Cumecs

Design discharge of the stream = 30.28Cumecs

II)Discharge from surplus wier of tank:-

Assume head of flow = 0.45m (As enquired from local people)

Length of check dam = 22.75m

The discharge per metre length of check dam is calculated as given below:-

24.13Cusecs 0.68Cumecs

(Where Cd =4.10 as being adopted by Irrigation authorities )

Hence the total discharge over the check dam = Q2 = 15.47Cumecs

Design Discharge = 45.75Cumecs

Design Velocity = 2.58m/sec

Ventway Calculations & fixation of RTL:-

provide a vent area of about 40 percent but not less than 30 percent of the unobstructed area of the stream measured between the proposed road top level and the stream bed.However, the available area of flowunder design HFL condition should always be at least 70 percent of the unobstructed area of flow between the design HFL and the stream bed i.e. the obstruction under design HFL condition should not be more than 30per cent.

Trial 1:-

Assume RTL of +5.645m,the unobstructed area of the stream measured between the RTL andstream bed (from graphical calculation in AUTOCAD) = 66.53sqm

To avoid debris and other tree logs etc.getting clogged in the vents,it is proposed to provide 6mspans,for which open expansion joints are sufficient.Hence,3 spans of each 6m are proposed.Further 4Nos of 900mm dia are proposed on each side of the spans to avoid concentration of flow in the middle portion,thereby avoiding the formation of eddies and scouring of face walls.

Vented area available for middle span = 6.88sqm

---do---- for left side span = 5.75sqm

---do---- for right side span = 5.95sqm

Cumulative area of vents available from = 7.63sqm900mm dia pipes

Total vented area provided = 26.21sqm

Percentage of vented area provided = 39.40% >30%

Using Dicken's formula Discharge Q = CA3/4 =

q = Cd L h3/2. =

As per caluse 5.1.3(ii)a of IRC SP:82-2008,low level submersible structures like causeways,

Hence O.K

From local enquiry,the HFL is fixed as +6.235m

Total area between HFL and stream bed for defined cross section = 79.33sqm(from graphical calculation in AUTOCAD)

Area available for flow in between HFL and RTL/PBL = 30.06sqm

Total vented area provided = 26.21sqm

Hence.total area available, when the flow is at HFL = 56.27sqm

Percentage of obstruction = 29.07% <30%

Hence O.K

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

Un obstructed area of cross section = A = 79.33Sqm

Total vented area provided = a = 56.27Sqm

Design discharge Q = 45.75Cumecs

Linear water way L = 28.80m

0.80m

Width of the channel at HFL = 45.38m

Using Orifice formula for calculation of discharge

In the present case,

a/A = 0.71

0.867Corresponding to this value the coefficient e from IRC SP:13--2004 = 0.91

Hence

0.2673499 = h+ 0.09734964322

At just upstream of the bridge

1.0081534 = (0.80+h) X u

u = 1.00815337153 ----------------(2)(0.80+h)

Substituting,the above value in eq (1) '2

0.2673499 = h+ 0.097350 X 1.008153

Depth of down stream water Dd =

Case(a) Assume that afflux is less than 1.4Dd:-

Q = Co X (2g)1/2 X L X Dd X [h+(1+e)u2/2g]1/2

Corresponding to this value the coefficient Co from IRC SP:13--2004 =

u2 ------------- (1)

Q = W X (Dd + h) X u

(0.80+h)

Solving by trial and error method,assume h = 0.30m

0.267350 = 0.33376490624426 Not satisfied

assume h = 0.131m

0.267350 = 0.26776523434566

Hence afflux h = 0.131m

Velocity u = 1.083m/sec

Applying Broad crested wier formula,

0.94

Hence H = 0.99m

0.99m

u = 1.018m/sec

0.937

0.137

From the above calculations,it is inferred that afflux is less than 1/4 th Dd and hence afflux to be adopted is from the Orifice formula,which is equal to 0.131m

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 = 60.85Cumecs

2.00

Discharge per metre width of foundations = q = 2.113

1.75m

2.63m(For design of abutment foundations,as per clause 110.1.4.2 of IRC:5--1985)

Case(b) Assume that afflux is more than 1.4Dd:-

Q = 1.706 CW LH3/2

As per clause 15.2 of IRC SP:13-2004,the value of CW for narrow bridge opening with or without floor =

H = Du + u2/2g ≈ Du

Du =

Again applying Q = Du x W x u

Du = H - u2/2g

Hence, Du =

Hence afflux h = Du - Dd =

Lacey's Silt factor ' f ' = 1.76Xm1/2(Due to pebbles&boulders in the bed) =

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

Maximum scour depth Dm = 1.5XD =

3.83m

Bottom level of foundation = 2.41m

Depth of foundation below low bed level = 1.56m

The Minimum Safe Bearing capacity of the soil is considered as 15 KN/m2 at a depth of 1.50m below LBL

Hence open foundation in the form of individual footings is proposed at a depth of 1.80m below LBL,ie,at a level of +2.315m

As the foundations are proposed below the Max.scour level,bed protection is not needed from scour depth considerations.

Design of Protection works:-

Afflux = 0.131m

Depth of flow = 2.27m

Head due to velocity of approach = 0.303m

Combined head due to Velocity of approach and 0.434mafflux

2.63m/sec

Linear water way required 7.67m <28.80m

Area available for flow at H.F.L = 56.27sqm

As per the clause 6.4.2(i),of IRC SP:82-2008,the post construction velocity under the structure should not exceed

protective works.

2.00m/sec

Discharge,that can be passed over the causeway safely = 112.54Cumecs >60.85

Hence O.K

As per the clause 5.1.3(iv),of IRC SP:82-2008 for the beds consisting of boulders upto 200mm size,the permissible velocity through vents is 2.5m/s and for beds containing larger sized boulders or rocky strata permissible velocity is 6m/s.

As the bed of the proposed stream is rocky strata,increased velocity of 2.68m/sec is allowed through vents withoutrigid floor protection.Hence rigid floor protection is not proposed.

However,suitably designed flexible aprons with cut-off walls are proposed on both upstream and down stream sides to protect against the probable eddies formed due to uneven spacing of vents along the causeway.

Design of cut-off walls/Toe walls:-

Though,it is sufficient to take the D/S side cut-off upto 1.27 times the normal scour depth as per caluse 703.2.3.2 of IRC 78-1983 considering that the reach is straight.

1.27XNormal scour depth from HFL = 2.22m

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

di =

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

hi =

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

LWW = Qd/(VvXdi) =

2 m/s and the intensity of discharge is limited to 3m3/m except in the case of properly designed raft foundation with adequate

Hence Vlim. =

Depth of bottom of Cut-off wall from HFL = 2.22m

Bottom level of cut-off wall = 4.01

Depth of bottom of D/S side Cut-off wall from LBL -0.05m

As per the clause 6.4.2(v),of IRC SP:82-2008,the minimum depth of cut-off wall on U/S side is 2.0m below bed level and 2.5m below bed level on D/S side.

Depth of bottom of D/S side Cut-off wall from LBL 2.50m

Depth of bottom of U/S side Cut-off wall from LBL 2.00m

As rigid floooring is not being proposed,there is no need to provide cut-off walls.But toe walls are proposed to a depth of 0.90m to protect the flexible apron.

Design of LAUNCHING/FLEXIBLE APRONS:-

Size of stones as per clause 5.3.7.2 of IRC 89-1985

0.28mSay 0.30m

Weight of each stone considering the specific gravity of stone as 2.65

37.48Kg

Say 40Kg

Weight of each stone shall not be less than 40 Kg.

Dimensions of apron as per clause 5.3.5.2 of IRC 89-1985

0.236

Thickness of apron at inner edge(near raft) = 1.5 x T = 0.354m

Say 0.60m

Thickness of apron at outer edge = 2.25 x T = 0.531m

Say 0.90m

Hence provide a thickness of 0.60m at near end and 0.9m at the outer end

Width of Launching Apron on U/S Side:-

The launching aprons are designed to reach a level of 1.50 times the normal scour depth

1.5 x D = 2.625m

Bottom level of apron after launching = HFL-1.5 X D = 3.61m

Depth below top of the raft = -1.65m

The apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89

Hence the width of launching apron at U/S = -3.30m

Diametre (d) = (Vmax/4.893)2 =

Weight of stone =4/3x x(d/2)3 x 2.65 x 1000 =

( T ) = 0.06 x (Qdf)1/3 =

As per the clause 6.4.2(vi),of IRC SP:82-2008,minimum width = 4.0m

Width of Launching Apron on D/S Side:-

The launching aprons are designed to reach a level of 2.00 times the normal scour depth

2.0 x D = 3.500m

Bottom level of apron after launching = HFL-2 X D = 2.74m

Depth below top of the raft = 0.23m

The apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89

Hence the width of launching apron at D/S = 0.46m

As per the clause 6.4.2(vi),of IRC SP:82-2008,minimum width = 6.0m

type design of submersible causeway

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