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Design of RCC SLAB BRIDGES
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Construction of 10.00mts span culvert at 5/6 KM of Vemuladeevi channel
Name of the work:-Construction of bridge across Dharbharevu canalon Gopuram road near Anjaneyaswamy temple in Pedalanka(V)
Construction of 10.00mts span culvert at 5/6 KM of Vemuladeevi channel
Name of the work:-Construction of bridge across Dharbharevu canalon Gopuram road near Anjaneyaswamy temple in Pedalanka(V)
Design Philosophy:-
The design of 1V-- 10.37m right span culvert is carried as per the procedure out lined
below:-
Step1:-
The design discharge was fixed after arriving discharge based on the following methods:-
and area by considering actual cross-section of the channel.
Step2:-
The vertical clearence and afflux are verified.
below the maximum scour depth
Step3:-
The structural components are desined in the following manner:-
and culverts of medium importance is selected.
designed as per the guide lines given in relevent IRC codes.
a.As per the hydraulic particulars furnished by the Irrigation department
b.By Area-Velocity method using Manning's equation for arriving at the flow velocity
a.Hydraulic particulars like HFL,OFL are obtained from Irrigation department.
b.Bottom of deck level was fixed based on HFL and road formation levels on both sides.
c.Ventway calculations are done for fixation of ventway.
d.Normal scour depth with reference to HFL was calculated using Lacey's equations
e.After arriving at the Maximum scour depth,bottom level of the foundation was fixed
After arriving at bottom of deck level,bottom of foundation level and required ventway,the dimensions of the bridge are finalised.
a.As per the recommendations of IRC 6:2000,IRC class A live load required for bridges
b.Load combination is selected as per IRC 6:2000
c.Based on the trial pit particulars and soil test reports,type of foundation was selected.
d.The structural components like Abutment,raft foundation are
e.The deck slab is proposed as per the MOST drawing Nos.BD 3-74&BD 4-74
f.The dirt wall is proposed as per the drawings given in Plate No.7.25 of IRC:SP20-2002(Rural roads manual)
Design of Abutments
I)Design Parameters:-
Clear Right Span = 10.00m
= 10.740m
Width of the carriage way = 5.50m
= 0.790m
= 0.075m
= 1.200m
Thickness of dirt wall = 0.30m
Sectional area of dirt wall = 0.440sqm
Thickness of RAFT footing = 0.70m
Height of abutments = 1.664m
(As per hydralic calculations)
Top width of abutments = 0.690m
Bottom width of abutments = 2.00m
Sectional area of abutment section = 2.238sqm
Bank side batter of abutment = 1.310m
Stream side batter of abutment = 0.000m
Width of 1st footing = 2.30m
Thickness of 1st footing = 0.30m
= 0.15m
Bank side offset of 1st footing wrt abutment = 0.15m
= 2.45m
= 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 = 6.55m
= 0.60m
Type of bearings = No bearings proposed
= 25KN/cum
= 24KN/cum
= 18KN/Cum
= 10KN/Cum
Deck slab length
Thickness of deck slab as per MOST Dg.BD 3-74
Thickness of wearing coat
Height of railing
Canal side offset of 1st footing wrt abutment
Width of 2nd footing
Thickness of 2nd footing
Canal side offset of 2nd footing wrt abutment
Thickness of VRCC RAFT footing
Unit weight of RCC (yrc)
Unit weight of PCC (ypc)
Density of back fill soil behind abutments (y)
Unit weight of water (yw)
= 30
= 51.81
= 0
= 15
= 1.20m
= 2.862m
= 0.488m
= 1.488m
= -1.512m
= 6.00t/sqm
= 25.00N/sqmm
= 415.00N/sqmm
Cover to reinforcement = 50.00mm
II)General loading pattern:-
As per IRC:6---2000,the following loadings are to be considered on the bridge or slabculvert:-
1.Dead load2.Live load3.Impact load4.Wind load5.Water current6.Tractive,braking effort of vehicles&frictional resistance of bearings7.Buoyancy8.Earth pressure9.Seismic force10.Water pressure force
As per clause 202.3,the increase in permissible stresses is not permissible for theabove loading combination.
III)Loading on the slab culvert for design of abutments:-
1.Dead Load:-
i)Self wieght of the deck slab = 583.32KN
ii)Self wieght of dirtwall over abutment = 60.50KN
iii)Self weight of wearing coat = 55.38KN
699.20KN
There is no need to consider snow load as per the climatic conditions
Angle of shearing resistance of back fill material(Q)
Angle of face of wall supporting earth with horizontal(In degrees)(in clock wise direction)(a)
Slope of back fill (b)
Angle of wall friction (q)
Height of surcharge considered (h3)
Road crest level (RTL)
Low bed level (LBL)
High flood Level (HFL)Bottom of foundation level (BFL) Safe Bearing Capacity of the soil (SBC)
Compressive strength of concrete for RCC Strip footing (fck)
Yield strength of steel (fy)
Self wieght of the abutments upto bottom most footing based on the preliminary section assumed:-
iv)Self wieght of the abutment section = 295.42KN
v)Self wieght of top footing = 91.08KN
vi)Self wieght of 2nd footing = 97.02KN
vii)Self wieght of 3rd footing = 0.00KN
viii)Self wieght of 4th footing = 0.00KN
483.52KN
ix)Calculation of eccentricity of self weight of abutment w.r.t base of abutment
S.No Description Load in KN Moment
1 143.86944 1.127 162.14
2 151.55712 0.345 52.29
3 0 0 0
295.42656 214.43
Location of resultant from toe of abutment = 0.73m
Distance of centroid of load from toe of abutment
Back batter(W1)
Centre portion(W2)
Front batter(W3)
W1W1
Eccentricity wrt centre of base of abutment = 0.270m
x)Calculation of eccentricity of self weight of abutment&1st footing w.r.t bottom of 1st footing
S.No Description Load in KN Moment
1 Back batter 143.86944 1.277 183.72
2 Centre portion 151.55712 0.495 75.02
3 Front batter 0 0 0
4 1st footing 91.08KN 1.15 104.74
386.50656 363.48
Location of resultant from toe of abutment = 0.94m
Eccentricity wrt centre of 1st footing= 0.210m
xi)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 2nd footing
Distance of centroid of load from toe of 1st footing
S.No Description Load in KN Moment
1 Back batter 143.86944 1.427 205.3
2 Centre portion 151.55712 0.645 97.75
3 Front batter 0 0.3 0
4 1st footing 91.08KN 1.300 118.4
5 2nd footing 97.02KN 1.225 118.85
483.52656 540.3
Location of resultant from toe of abutment = 1.12m
Eccentricity = 0.105m
xii)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 2nd footing
S.No Description Load in KN Moment
1 Back batter 0 1.427 02 Centre portion 0 0.645 03 Front batter 0 0.3 04 1st footing 0 1.00 05 2nd footing 0 0.92 06 3rd footing 0 0.00 0
0 0
Location of resultant from toe of abutment = 0.00m
Eccentricity = 0.000m
2.Live Load:-
As per clause 201.1 of IRC:6--2000,the bridges and culverts of medium importance
GENERAL IRC Class-A loading Pattern
Distance of centroid of load from toe of 2nd footing
Distance of centroid of load from toe of 3rd footing
are to be designed for IRC Class A loading.
2.7t
2.7t
11.4
t
11.4
t
6.8t
6.8t
6.8t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
2.7t
2.7t
11.4
t
11.4
t
6.8t
6.8t
6.8t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
clauses 207.1.3&207.4
The ground contact area of wheels for the above placement,each axle wise isgiven below:-
Axle load Ground Contact Area(Tonnes) B(mm) W(mm)
11.4 250 5006.8 200 380
The IRC Class A loading as per the drawing is severe and the same is to be considered as per
Y
X
11.4t
11.4t
6.8t
6.8t
475
5500
Portion to be loadedwith 5KN/m² liveload
10000
35252925
11380
2.7 150 200
Assuming 0.475m allowance for guide posts/kerbs and the clear distance of vehicle from
the edge of guide post being 0.15m as per clause 207.1,the value of 'f' shown in the figure will
be 0.625m
0.625m
3.525m
4.15m
The total live load on the deck slab composes the following components:-
1.Wheel loads----Point loads 364.00KN
2.Live load in remaing portion(Left side)----UDL 33.56KN
2.Live load in remaing portion(Right side)----UDL 189.29KN
586.86KN
Resultant live load:-
Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)
Taking moments of all the forces w.r.t y-axis
S.No Distance from Y-axis Moment
1 57 0.875m 49.88KNm
2 57 0.875m 49.88KNm
3 57 2.675m 152.48KNm
4 57 2.675m 152.48KNm
5 34 0.875m 29.75KNm
6 34 0.875m 29.75KNm
7 34 2.675m 90.95KNm
8 34 2.675m 90.95KNm
9 33.5625 0.313m 10.49KNm
10 189.2925 4.688m 887.31KNm
Hence,the width of area to be loaded with 5KN/m2 on left side is (f) =
Similarly,the area to be loaded on right side (k) =
Wheel Load/UDL in KN
586.855 1543.90KNm
Distance of centroid of forces from y-axis
= 2.631m
Eccentricity = 0.594m
Eccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)
Taking moments of all the forces w.r.t x-axis
S.No Load in KN Distance from X-axis Moment
1 57 11.005m 627.29KNm
2 57 11.005m 627.29KNm
3 57 9.805m 558.89KNm
4 57 9.805m 558.89KNm
5 34 5.505m 187.17KNm
6 34 5.505m 187.17KNm
7 34 2.505m 85.17KNm
8 34 2.505m 85.17KNm
9 33.56KN 5.690m 190.97KNm
10 189.29KN 5.690m 1077.07KNm
586.855 4185.06KN
Distance of centroid of forces from x-axis
= 7.131m
Eccentricity = 2.441m
Y
X5500
10000
Location of Resultant
2631
7131
11380
Calculation of reactions on abutments:-
367.74KN
219.12KN
Hence,the critical reaction is Ra = 367.7KN
The corrected reaction at obtuse corner = 367.74KN
Assuming that the live load reaction acts at the centre of the contact area on the abutment,
Reaction due to loads Ra =
Reaction due to point loads = Rb =
300
300
185
815815
740
Y
X5500
10000
Location of Resultant
2631
7131
11380
The eccentricty of the line of action of live load at bottom of abutment = 0.815m
----do----on top of 1st footing = 0.815m
----do----on top of 2nd footing = 0.740m
The eccentricity in the other direction need not be considered due to high section modulus in transverse direction.
3.Impact of vehicles:-
As per Clause 211 of IRC:6--2000,impact allowance shall be made by an increment
of live load by a factor 4.5/(6+L)
Hence,the factor is 0.269
Further as per clause 211.7 of IRC:6--2000,the above impact factor shall be only
50% for calculation of pressure on piers and abutments just below the level of bed block.There
is no need to increase the live load below 3m depth.
As such,the impact allowance for the top 3m of abutments will be 0.1345
For the remaining portion,impact need not be considered.
4.Wind load:-
The deck system is located at height of (RTL-LBL) 2.37m
The Wind pressure acting on deck system located at that height is considered for design.
As per clause 212.3 and from Table .4 of IRC:6---2000,the wind pressure at that hieght is=
59.48
Height of the deck system = 2.065
Breadth of the deck system = 11.38
Kg/m2.
300
300
185
815815
740
The effective area exposed to wind force =HeightxBreadth =
Hence,the wind force acting at centroid of the deck system = 6.97KN(Taking 50% perforations)
Further as per clause 212.4 of IRC:6---2000 ,300 Kg/m wind force is considered to be
acting at a hieght of 1.5m from road surface on live load vehicle.
Hence,the wind force acting at 1.5m above the road surface = 16.50KN
The location of the wind force from the top of RCC raft footing = 4.93m
5.Water current force:-
Water pressure considered on square ended abutments as per clause 213.2 of IRC:6---2000 is
26.286
(where the value of 'K' is 1.5 for square ended abutments)
For the purpose of calculation of exposed area to water current force,only 1.0m
width of abutment is considered for full hieght upto HFL
Hence,the water current force = 0.62KN
Point of action of water current force from the top of RCC raft footing = 3.77m
6.Tractive,braking effort of vehicles&frictional resistance of bearings:-
The breaking effect of vehicles shall be 20% of live load acting in longitudinal
direction at 1.2m above road surface as per the clause 214.2 of IRC:6--2000.
As no bearings are assumed in the present case,50% of the above longitudinal
force can be assumed to be transmitted to the supports of simply supported spans resting on
stiff foundation with no bearings as per clause 214.5.1.3 of IRC:6---2000
Hence,the longitudinal force due to braking,tractive or frictional resistance of
bearings transferred to abutments is
58.69KN
The location of the tractive force from the top of RCC raft footing = 4.63m
7.Buoyancy :-
P = 52KV2 = Kg/m2.
As per clause 216.4 of IRC:6---2000,for abutments or piers of shallow depth,the dead weight of the abutment shall be reduced by wieght of equal volume of water upto HFL.
The above reduction in self wieght will be considered assuming that the back fill behind the abutment is scoured.
For the preliminary section assumed,the volume of abutment section is
i)Volume of abutment section = 12.31Cum
ii)Volume of top footing = 3.80Cum
iii)Volume of 2nd footing = 4.04Cum
iv)Volume of 3rd footing = 0.00Cum
v)Volume of 4th footing = 0.00Cum
20.15Cum
Reduction in self wieght = 201.47KN
8.Earth pressure :-
As per clause 217.1 of IRC:6---2000,the abutments are to be designed for a
surcharge equivalent to a back fill of hieght 1.20m behind the abutment.
The coefficient of active earth pressure exerted by the cohesion less back fill on
the abutment as per the Coulomb's theory is given by
'2Sin(a+Q)
sina sin(a-q) sin(Q+q)sin(Q-b)
sin(a+b)
Sin(a+Q) = SIN[3.14*(51.81+30)/180] = 0.99Sin(a-q) = SIN[3.14*(51.81-15)/180] = 0.599Sina = SIN[3.14*(51.81)/180] = 0.786Sin(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*(51.81+0)/180] = 0.786
From the above expression,
0.76
The hieght of abutment above GL,as per the preliminary section assumed = 1.664m
Hence,maximum pressure at the base of the wall Pa = 22.76KN/sqm
Ka =
Ka =
The pressure distribution along the height of the wall is as given below:-
Surcharge load = 16.42 KN/sqm
16.42
1.664
22.76 16.42
Area of the rectangular portion = 27.32Area of the triangular portion = 18.94
46.26
Taking moments of the areas about the toe of the wall
S.No Description Area Lever arm Moment
1 Rectangular 27.32 0.832 22.730242 Triangular 18.94 0.55466667 10.50538667
46.26 33.23562667
Height from the bottom of the wall = 0.72m
The active Earth pressure acts on the abutment as shown below:-
0.70
53.191.664m
0.72m
51.81
2.000.57
Total earth pressure acting on the abutment P = 254.43KN
152.54KN
203.63KN
Eccentricity of vertical component of earth pressure = 0.43m
9.Siesmic force :-
As per clause 222.1 of IRC:6---2000,the bridges in siesmic zones I and II need not be
designed for siesmic forces.The location of the slab culvert is in Zone-I.Hence,there is no need to
design the bridge for siesmic forces.
10.Water pressure force:-
The water pressure distribution on the abutment is as given below:-
HFL 1.488m
3.00
BFL -1.512m
Horizontal component of the earth pressure Ph =
Vertical component of the earth pressure Pv =
30.00kn/sqm
Total horizontal water pressure force = 247.50KN
The above pressure acts at height of H/3 = 1.00m
IV)Check for stresses for abutments&footings:-
a)Load Envelope-I:-(The Canal is dry,back fill scoured with live load on span)
i)On top of RCC raft
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 699.20KN -0.740 0.00
2 Self wieght of abutment&footings 483.53KN 0.105 0.000
3 466.66KN -0.740 0.000
4 Impact load 0.00 0.00 0.00
1649.38
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.93
2 Tractive,Braking&Frictional resistance of bearings 58.69KN y-Direction 4.63
3 Water current force 0.62KN x-Direction 3.77
Check for stresses:-
About x-axis:-
Breadth of 2nd footing b = 6.25m
Depth of 2nd footing d = 2.45m
Area of the footing = A = 15.3125
Section modulus of bottom footing 6.25
about x-axis --Zx =
Vertical forces acting on the abutment (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Reaction due to live load with impact factor---(Wheel loads+UDL)
Horizontal forces acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN -0.740 13.222 Self wieght of abutment&footings 483.53KN 0.105 34.763 Reaction due to live load with impact factor 466.66KN -0.740 8.834 Impact load 0.00KN 0.000 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 58.69KN 4.63 -43.46
13.35
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.740 78.12 Self wieght of abutment&footings 483.53KN -0.105 28.393 Reaction due to live load with impact factor 466.66KN 0.740 52.134 Impact load 0.00KN 0.000 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 58.69KN 4.63 43.46
202.08
Stress at heel = P/A(1+6e/b)+M/Z = 13.35 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 202.08 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 3rd footing b = 2.45m
Depth of 3rd footing d = 6.25m
Area of the footing = A = 15.3125
Section modulus of bottom footing about = 15.95
y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at heelP/A(1+6e/b)
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 45.662 Self wieght of abutment&footings 483.53KN 0.00 31.583 Reaction due to live load with impact factor 466.66KN 0.000 30.484 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.93 -5.16 Water current force 0.62KN 3.77 -0.15
102.47
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 45.662 Self wieght of abutment&footings 483.53KN 0.00 31.583 Reaction due to live load with impact factor 466.66KN 0.000 30.484 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.93 5.16 Water current force 0.62KN 3.77 0.15
112.97
Stress at up stream side P/A(1+6e/b)+M/Z = 102.47 KN/Sqm>-2800KN/sqm.edge =
Hence safe.
Stress at down stream side P/A(1+6e/b)+M/Z = 112.97 KN/Sqm<5000KN/sqmedge =
Hence safe.
i)On top of 2nd footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 699.20KN -0.740 0.00
2 Self wieght of abutment&cut waters 386.51KN 0.210 0.000
3 Reaction due to live load with impact factor 466.66KN -0.740 0.000
4 Impact load 0.00 0.000 0.00
Intensity in KN (P)
Eccentricity/Lever arm
Stress at upstream edgeP/A(1+6e/b)
Intensity in KN (P)
Eccentricity/Lever arm
Stress at D/S edgeP/A(1+6e/b)
Vertical load acting on the abutment (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.63
2 Tractive,Braking&Frictional resistance of bearings 58.69KN y-Direction 4.33
3 Water current force 0.62KN x-Direction 3.47
Check for stresses:-
About x-axis:-
Breadth of 1st footing b = 6.25mDepth of 1st footing d = 2.30mArea of the footing = A = 14.375
Section modulus of base of abutment 5.51
about x-axis--Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN -0.74 14.092 Self wieght of abutment&footings 386.51KN 0.21 29.243 Reaction due to live load with impact factor 466.66KN -0.74 9.44 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 58.69KN 4.33 -46.11
6.62
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.74 83.192 Self wieght of abutment&footings 386.51KN -0.21 21.473 Reaction due to live load with impact factor 466.66KN 0.74 55.534 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 58.69KN 4.33 46.11
206.3
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
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)
Stress at heel = P/A(1+6e/b)+M/Z = 6.62 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 206.3 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 2.30mDepth of 1st footing d = 6.25mArea of the footing = A = 14.375
Section modulus of base of abutment 14.97
about y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 48.642 Self wieght of abutment&footings 386.51KN 0.00 26.893 Reaction due to live load with impact factor 466.66KN 0.000 32.464 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.63 -5.16 Water current force 0.62KN 3.47 -0.14
102.75
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 48.642 Self wieght of abutment&footings 386.51KN 0.00 26.893 Reaction due to live load with impact factor 466.66KN 0.000 32.464 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.63 5.16 Water current force 0.62KN 3.47 0.14
113.23
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 102.75 KN/Sqm>-2800KN/sqm.
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 -2N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at upstream edgeP/A(1+6e/b)
Intensity in KN (P)
Eccentricity/Lever arm
Stress at D/S edgeP/A(1+6e/b)
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 113.23 KN/Sqm<5000KN/sqm
Hence safe.
i)On top of 1st footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehiclesb)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 699.20KN -0.815 0.002 Self wieght of abutment&footings 295.43KN 0.270 0.0003 Reaction due to live load with impact factor 466.66KN -0.815 0.000
4 Impact load 0.00 0.000 0.00
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.332 Tractive,Braking&Frictional resistance of bearings 58.69KN y-Direction 4.033 Water current force 0.62KN x-Direction 3.17
Check for stresses:-
About x-axis:-
Breadth of abutment b = 6.25mDepth of abutment d = 2.00mArea of the footing = A = 12.5
Section modulus of base of abutment 4.17
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
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
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)
1 Reaction due to dead load from super structure 699.20KN -0.82 12.172 Self wieght of abutment&footings 295.43KN 0.27 26.73 Reaction due to live load with impact factor 466.66KN -0.82 8.124 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 58.69KN 4.03 -56.76
-9.77
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.82 99.72 Self wieght of abutment&footings 295.43KN -0.27 17.513 Reaction due to live load with impact factor 466.66KN 0.82 66.544 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 58.69KN 4.03 56.76
240.51
Stress at heel = P/A(1+6e/b)+M/Z = -9.77 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 240.51 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of abutment b = 2.00mDepth of abutment d = 6.25mArea of the footing = A = 12.5
Section modulus of base of abutment 13.02
about y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 55.942 Self wieght of abutment&footings 295.43KN 0.00 23.633 Reaction due to live load with impact factor 466.66KN 0.000 37.33
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
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 upstream edgeP/A(1+6e/b)
4 Impact load 0.00KN 0.00 0Horizontal loads:- (Stress = M/Z)
5 Wind load 16.50KN 4.33 -5.496 Water current force 0.62KN 3.17 -0.15
111.26
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 55.942 Self wieght of abutment&footings 295.43KN 0.00 23.633 Reaction due to live load with impact factor 466.66KN 0.000 37.334 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.33 5.496 Water current force 0.62KN 3.17 0.15
122.54
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 111.26 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 122.54 KN/Sqm<5000KN/sqm
Hence safe.
b)Load Envelope-II:-(The Canal is full,back fill intact with no live load on span)
i)On top of RCC Raft footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 699.20KN -0.740 0.00
Self wieght of abutment&cut waters 483.53KN
Reduction in self weight due to buoyancy -201.47KN
2 Net self weight 282.06KN 0.105 0.000
3 Vertical component of earth pressure 203.63KN 0.430 0.000
Intensity in KN (P)
Eccentricity/Lever arm
Stress at D/S edgeP/A(1+6e/b)
Vertical load acting on the abutment (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.93
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Water current force 0.62KN x-Direction 3.77
4 Horizontal load due to earth pressure 152.54KN y-Direction 1.32
5 Water pressure force 247.50KN y-Direction 1.00
Check for stresses:-
About x-axis:-
Breadth of bottom footing b = 6.25mDepth of bottom footing d = 2.45mArea of the footing = A = 15.3125
Section modulus of bottom footing 6.25
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN -0.74 13.222 Net self wieght of abutment&footings 282.06KN 0.10 20.283 Vertical component of Earth pressure 203.63KN 0.43 18.79
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 152.54KN 1.32 -32.175 Water pressure force 247.50KN 1.00 39.6
59.7
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.74 78.12 Net self wieght of abutment&footings 282.06KN -0.10 16.563 Vertical component of Earth pressure 203.63KN -0.43 7.81
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 152.54KN 1.32 32.175 Water pressure force 247.50KN 1.00 -39.6
95.06
Stress at heel = P/A(1+6e/b)+M/Z = 59.7 KN/Sqm>-2800KN/sqm.
Intensity in KN
Location(Ht.from the section considered).(m)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
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)
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 95.06 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of bottom footing b = 2.45mDepth of bottom footing d = 6.25mArea of the footing = A = 15.3125
Section modulus of bottom footing 15.95
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 45.662 Net self wieght of abutment&footings 282.06KN 0.00 18.423 Vertical component of Earth pressure 203.63KN 0.00 13.3
Horizontal loads:- (Stress = M/Z)4 Wind load 16.50KN 4.93 -5.15 Water current force 0.62KN 3.77 -0.2
72.13
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 45.662 Net self wieght of abutment&footings 282.06KN 0.00 18.423 Vertical component of Earth pressure 203.63KN 0.00 13.3
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 4.93 5.15 Water pressure force 0.62KN 3.77 0.2
82.63
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 72.13 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 82.63 KN/Sqm<5000KN/sqm
Hence safe.
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 U/S EdgeP/A(1+6e/b)
Intensity in KN (P)
Stress at D/S edgeP/A(1+6e/b)
ii)On top of 2nd footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 699.20KN -0.74 0.00
Self wieght of abutment&footings 483.53KN
Reduction in self weight due to buoyancy -201.47KN
2 Net self weight 282.06KN 0.105 0.000
3 Vertical component of earth pressure 203.63KN 0.430 0.000
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.63
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Water current force 0.62KN x-Direction 3.47
4 Horizontal load due to earth pressure 152.54KN y-Direction 1.02
5 Water pressure force 247.50KN y-Direction 0.70
Check for stresses:-
About x-axis:-
Breadth of 2nd footing b = 6.25mDepth of 2nd footing d = 2.30mArea of the footing = A = 14.375
Section modulus of bottom footing 5.51
about 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
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
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)
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN -0.74 14.092 Net self wieght of abutment&footings 282.06KN 0.10 21.63 Vertical component of Earth pressure 203.63KN 0.43 20.01
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 152.54KN 1.02 -28.195 Water pressure force 247.50KN 0.70 31.4
58.95
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.74 83.192 Net self wieght of abutment&footings 282.06KN -0.10 17.643 Vertical component of Earth pressure 203.63KN -0.43 8.32
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 152.54KN 1.02 28.195 Water pressure force 247.50KN 0.70 -31.4
105.9
Stress at heel = P/A(1+6e/b)+M/Z = 58.95 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 105.9 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 2.30mDepth of 1st footing d = 6.25mArea of the footing = A = 14.375
Section modulus of bottom footing 14.97
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 48.642 Net self wieght of abutment&footings 282.06KN 0.00 19.623 Vertical component of Earth pressure 203.63KN 0.00 14.17
Horizontal loads:- (Stress = M/Z)4 Wind load 16.50KN 4.63 -5.1
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
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 U/S EdgeP/A(1+6e/b)
5 Water current force 0.62KN 3.47 -0.177.19
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 48.642 Net self wieght of abutment&footings 282.06KN 0.00 19.623 Vertical component of Earth pressure 203.63KN 0.00 14.17
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 4.63 5.15 Water pressure force 0.62KN 3.47 0.1
87.67
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 77.19 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 87.67 KN/Sqm<5000KN/sqm
Hence safe.
iii)On top of 1st footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 699.20KN -0.74 0.00
Self wieght of abutment&cut waters 386.51KN
Reduction in self weight due to buoyancy -161.04KN
2 Net self weight 225.46KN 0.210 0.000
3 Vertical component of earth pressure 203.63KN 0.430 0.000
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.33
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Water current force 0.62KN x-Direction 3.17
Intensity in KN (P)
Stress at D/S edgeP/A(1+6e/b)
Vertical load acting on the abutment (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
4 Horizontal load due to earth pressure 152.54KN y-Direction 0.72
5 Water pressure force 247.50KN y-Direction 0.40
Check for stresses:-
About x-axis:-
Breadth of 1st footing b = 6.25mDepth of 1st footing d = 2.30mArea of the footing = A = 14.375
Section modulus of bottom footing 5.51
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN -0.74 14.092 Net self wieght of abutment&footings 225.46KN 0.21 18.853 Vertical component of Earth pressure 203.63KN 0.43 20.01
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 152.54KN 0.72 -19.895 Water pressure force 247.50KN 0.40 18.0
51.03
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.74 83.192 Net self wieght of abutment&footings 225.46KN -0.21 12.523 Vertical component of Earth pressure 203.63KN -0.43 8.32
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 152.54KN 0.72 19.895 Water pressure force 247.50KN 0.40 -18.0
105.95
Stress at heel = P/A(1+6e/b)+M/Z = 51.03 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 105.95 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 1st footing b = 2.30mDepth of 1st footing d = 6.25mArea of the footing = A = 14.375
Section modulus of bottom footing 14.97
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 48.642 Net self wieght of abutment&footings 225.46KN 0.00 15.683 Vertical component of Earth pressure 203.63KN 0.00 14.17
Horizontal loads:- (Stress = M/Z)4 Wind load 16.50KN 4.33 -4.775 Water current force 0.62KN 3.17 -0.1
73.59
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 699.20KN 0.00 48.642 Net self wieght of abutment&footings 225.46KN 0.00 15.683 Vertical component of Earth pressure 203.63KN 0.00 14.17
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 4.33 4.775 Water pressure force 0.62KN 3.17 0.1
83.39
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 73.59 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 83.39 KN/Sqm<5000KN/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)
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
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 U/S EdgeP/A(1+6e/b)
Intensity in KN (P)
Stress at D/S edgeP/A(1+6e/b)
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 699.20KN 0.82 0.00
2 Self wieght of abutments 295.42KN 0.270 0.000
3 Reaction due to live load with impact factor 466.66KN 0.82 0.000
4 Vertical component of Active Earth pressure 203.63KN 0.430 0.00
1664.91KN
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.33
2 Tractive,Braking&Frictional resistance of bearings 58.69KN y-Direction 4.33
3 Horizontal Active Earth pressure force 152.54KN y-Direction 0.72
227.73KN
Check for stability against over turning:-
Taking moments of all the overturning forces about toe of the abutment wrt x-axis,
Moment due to tractive,braking&frictional resistance of bearings = 254.11Kn-m
Moment due to active earth pressure force = 109.60Kn-m
Total overturning moment = 363.70Kn-m
Taking moments of all the restoring forces about toe of the abutment wrt x-axis,,
Moment due to self weight of abutment = 375.18Kn-m
Moment due to live load reaction on abutment = 846.99Kn-m
Moment due to super structure load reaction on abutment = 1269.04Kn-m
Moment due to vertical component of active earth pressure = 291.19Kn-m
Total Restoring moment = 2782.40Kn-m
Factor of safety = 7.65017071 > 2.0 Hence safe
Vertical load acting on the abutment (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
(As per clause 706.3.4 of IRC:78-2000)
Check for stability against sliding:-
1664.91KN
227.73KN
Coefficient of friction between concrete surfaces = 0.80
5.84879451 > 1.5 Hence safe
(As per clause 706.3.4 of IRC:78-2000)
b)Load Envelope-IV:-(The Canal is running upto HFL with no live load on span)
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 699.20KN 0.82 0.00
Self wieght of abutments 295.42KN
-123.10KN
2 Net self wieght 172.32KN 0.270 0.000
3 Vertical component of Active Earth pressure 203.63 0.430 0.00
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.33
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Active Earth pressure force 152.54KN y-Direction 0.72
4 Force due to water pressure 247.50KN y-Direction 0.40
Check for stability against over turning:-
Taking moments of all the overturning forces about toe of the abutment wrt x-axis,
Moment due to tractive,braking&frictional resistance of bearings = 0.00Kn-m
Moment due to active earth pressure force = 109.60Kn-m
Total vertical load acting on the base of the abutment Vb =
Total sliding force,ie,horizontal load on the abutment Hb =
Factor of safety against sliding Fs =
Vertical load acting on the abutment (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Reduction in self weight due to buoyancy
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
Total overturning moment = 109.60Kn-m
Taking moments of all the restoring forces about toe of the abutment wrt x-axis,
Moment due to self weight of abutment = 218.85Kn-m
Moment due to water pressure force on the abutment = 99.00Kn-m
Moment due to super structure load reaction on abutment = 1269.04Kn-m
Moment due to vertical component of active earth pressure = 291.19Kn-m
Total Restoring moment = 1878.08Kn-m
Factor of safety = 17.1362919 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)
Check for stability against sliding:-
623.45KN
152.54KN
Coefficient of friction between concrete surfaces = 0.80
3.26968769 > 1.5 Hence safe
(As per clause 706.3.4 of IRC:78-2000)
Total vertical load acting on the base of the abutment Vb =
Total sliding force,ie,horizontal load on the abutment Hb =
Factor of safety against sliding Fs =
DESIGN OF RAFT FOR THE SLAB CULVERT
Name of the work:-Slab culvert on 6/0 Km of Vemuladeevi Channel
Abutment
Abutment
Length of the Raft:- = 14.60m
Width of the Raft:- = 6.85m
Total load on the Raft:-
Dead Load:-
Wt.of Deck slab = 1166.63Kn
Wt.of wearing coat = 110.76Kn
Wt.of bed blocks over abutments = 121.00Kn
Wt.of abutments
Footing-I = 182.16KnFooting-II = 194.04KnWt.of abutments = 590.84Kn
Total 2365.43Kn
Dead load stress = 23.65Kn/Sqm
Live Load:-
Taking IRC Class-A loading
Wheel width in the direction of movement =0.2+0.2+0.25/2 = 0.625m
11.4 11.4 6.8 6.8
1.2 4.3 3.0 5.475
0.625
14.60m
Centre of gravity of loading from 1st 11.4t load =
= 2.99m
Centre of gravity from the end of raft = 3.615m
Eccentricity = 3.685m
Stress due to live load = 1xP(1+6e/b)(Taking single lanes) A
Max.stress = 15.08Kn/Sqm
Min.stress = -7.95Kn/Sqm
Total stress due to dead load and live load
Max.Stress = 38.73Kn/Sqm
Min.Stress = 15.70Kn/Sqm
Assuming the depth of raft as 70cm
Stress due to self weight of raft = 17.50Kn/Sqm
Stress due to wieght of base concrete = 3.60Kn/Sqm
Hence,the Max.stress on the soil = 59.83Kn/Sqm
Which is less than 6t/sqm(Soil testing report)
Hence safe.
Net Max.upward pressure acting on Raft = 38.73Kn/Sqm
Net Min.upward pressure acting on Raft = 15.70Kn/Sqm
The design stress = 27.21Kn/Sqm
Hence,the UDL on the raft = 27.21Kn/m
Design of Raft:-
The raft will be analysed as a continuous beam of 1m width with the loadingas shown below:-
1.375 11.85 1.375
UDL of 27.21Kn/m
After analysis the bending moment diagram is as given below:
678
38.6
Max.Negative bending moment Mu = 678.00KNm
Max.Positive bending moment Mu = 38.60KNm
Effective depth required d = 443.31mm
Over all depth provided = 700.00mm
Effective depth provided(Assuming 40mm cover) d = 637.50mm
Top steel:-
1.668
From table 3 of SP 16,percentage of steel required = 0.505
Area of steel required = 3219.38sqmm
Bottom steel:-
0.095
From table 3 of SP 16,percentage of steel required/Minimum steel = 0.12
Area of steel required = 765.00sqmm
Hence provide 12mm dia HYSD bars@ 125mm c/c spacing at bottom and provide 25mm bars at 150mm c/c at top
3270.83sqmm
904.32sqmm
Provide distribution reinforcement of 0.12% both at top and bottom
Area = 840.00sqmm
Mu/0.138fckb =
Mu/bd2 =
Mu/bd2 =
Hence Ast provided at top =
Hence Ast provided at bottom =
Adopting 12mm dia bars,the spacing required is = 134.57mm
Hence provide 12mm dia bars @ 125mm c/c spacing at top& bottom as distribution steel
DESIGN OF RAFT FOR THE SLAB CULVERT
Hydraulic design
Hydraulic Particulars:-
1.Full supply Level 1.488
2.Ordinary Flood level
3.Lowest Bed level 0.488
4.Average bed slope 0.000059(1 in 17000)
0.025(As per table 5 of IRC:SP 13)
6.Vertical clearence proposed 0.509(As per clause 15.5 of IRC:SP 13&as per profile)
6.Bottom of deck proposed 1.997(MFL+Vertical clearence)
7.Road Crest level 2.862(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 = 3.300Cumecs
2)Area Velocity method:-
Depth of flow w.r.t HFL = 1.000m
Bed width = 8.30m
Assuming side slopes 1:1.5 in clayey soils,top width at HFL = 9.800m
Wetted Area = 9.05sqm
Wetted perimetre = 11.13m
Hydraulic Radius R= Total area/Wetted perimeter = 0.81
Velocity V = 0.27m/sec
Discharge Q = AXV 2.44Cumecs
Design Discharge = 3.300Cumecs
Design Velocity = 0.337m/sec
5.Rugosity Coefficient(n)
1/nX(R2/3XS1/2)
Ventway Calculations(H.F.L Condition):-
Assuming the stream to be truly alluvial,the regime width is equal to linear waterway required for the drain.
8.72m
The actual top width is almost equal to the above regime width.Hence,the stream is almost truly alluvial in nature.As per IRC:SP--13,the ventway calculations for alluvial streams are as given below:-
Assuming afflux = x = 0.15m9.80m
Clear span = 10.00mEffective linear water way = 10.00m
Depth of flow = 1.00m
Head due to velocity of approach = 0.004m
Combined head due to Velocity of approach and 0.154mafflux
1.56m/sec
Linear water way required 2.11m
No.of vents required = = 0.211Say---1 Vent
In alluvial streams,the actual width of the stream should not be reduced,as it results in enhanced scour depth and expensive training works.
Hence No.of vents required as per the width of the stream at H.F.L= 0.98
No.of vents to be provided 1Nos
No.of piers = 0Nos
Scour Depth Calculations:-
As per the clause 101.1.2 of IRC:5--1985,the design discharge should be increased by 30% to ensure adequate margin of safety for foundations and protection works
Hence,the discharge for design of foundations = 1.30XDesign Discharge =
Discharge per metre width of foundations = q =
Hence,as per Lacey's silt theory,the regime width W = 4.8Q1/2 = 4.8*3.30.5 =
Width of channel at H.F.L(b+h) =
di =
(Vmax2/2g)X[di/(di+x)]2
hi =
Velocity through vents Vv = 0.90X(2ghi)1/2 =
LWW = Qd/(VvXdi) =
LWW /LC
Lacey's Silt factor ' f ' = 1.76Xm1/2(For normal silt) =
Normal scour depth D = 1.34(q2/f)1/3 =
Bottom level of foundation =
Depth of foundation below low bed level =
The Minimum Safe Bearing capacity of the soil is considered as 60 KN/m2 at a depth of 2.00m below LBL
Hence open foundation in the form of raft is proposed at a depth of 2.0m below LBL,ie,at a level of
Cut-off walls and aprons are not required from scour depth point of view
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
4.39Cumecs
1.00
0.439
0.78m
1.17m
2.37m
-0.88m
1.370m
-1.512m