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RCC Slab culvert
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Name of the work:-Road from R&B Road to SC colony of Pedalanka.
Construction of 6.00mts span culvert at 6/0 KM of Vemuladeevi channel
Design Philosophy:-
The design of 1V-- 6.37m right span culvert is carried as per the procedure out lined
below:-
Step1:-
The design discharge was fixed after arriving discharge based on the following methods:-
and area by considering actual cross-section of the channel.
Step2:-
The vertical clearence and afflux are verified.
below the maximum scour depth
Step3:-
The structural components are desined in the following manner:-
and culverts of medium importance is selected.
designed as per the guide lines given in relevent IRC codes.
a.As per the hydraulic particulars furnished by the Irrigation department
b.By Area-Velocity method using Manning's equation for arriving at the flow velocity
a.Hydraulic particulars like HFL,OFL are obtained from Irrigation department.
b.Bottom of deck level was fixed based on HFL and road formation levels on both sides.
c.Ventway calculations are done for fixation of ventway.
d.Normal scour depth with reference to HFL was calculated using Lacey's equations
e.After arriving at the Maximum scour depth,bottom level of the foundation was fixed
After arriving at bottom of deck level,bottom of foundation level and required ventway,the dimensions of the bridge are finalised.
a.As per the recommendations of IRC 6:2000,IRC class A live load required for bridges
b.Load combination is selected as per IRC 6:2000
c.Based on the trial pit particulars and soil test reports,type of foundation was selected.
d.The structural components like Abutment,raft foundation are
e.The deck slab is proposed as per the MOST drawing Nos.BD 1-74&BD 2-74
f.The dirt wall is proposed as per the drawings given in Plate No.7.25 of IRC:SP20-2002(Rural roads manual)
Design of Abutments
I)Design Parameters:-
Clear Right Span = 6.00m
= 6.740m
Width of the carriage way = 5.50m
= 0.515m
= 0.075m
= 1.200m
Thickness of dirt wall = 0.30m
Sectional area of dirt wall = 0.360sqm
Thickness of RAFT footing = 0.50m
Height of abutments = 1.804m
(As per hydralic calculations)
Top width of abutments = 0.690m
Bottom width of abutments = 2.00m
Sectional area of abutment section = 2.426sqm
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 1-74
Thickness of wearing coat
Height of railing
Canal side offset of 1st footing wrt abutment
Width of 2nd footing
Thickness of 2nd footing
Canal side offset of 2nd footing wrt abutment
Thickness of VRCC RAFT footing
Unit weight of RCC (yrc)
Unit weight of PCC (ypc)
Density of back fill soil behind abutments (y)
Unit weight of water (yw)
= 30
= 54.04
= 0
= 15
= 1.20m
= 2.577m
= 0.477m
= 1.477m
= -0.923m
= 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 = 238.64KN
ii)Self wieght of dirtwall over abutment = 49.50KN
iii)Self weight of wearing coat = 34.76KN
322.90KN
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 = 320.23KN
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
508.33KN
ix)Calculation of eccentricity of self weight of abutment w.r.t base of abutment
S.No Description Load in KN Moment
1 155.97384 1.127 175.78
2 164.30832 0.345 56.69
3 0 0 0
320.28216 232.47
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 155.97384 1.277 199.18
2 Centre portion 164.30832 0.495 81.33
3 Front batter 0 0 0
4 1st footing 91.08KN 1.15 104.74
411.36216 385.25
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 155.97384 1.427 222.57
2 Centre portion 164.30832 0.645 105.98
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
508.38216 565.8
Location of resultant from toe of abutment = 1.11m
Eccentricity = 0.115m
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
8000
3525
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 21.06KN
2.Live load in remaing portion(Right side)----UDL 118.79KN
503.86KN
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 21.0625 0.313m 6.58KNm
10 118.7925 4.688m 556.84KNm
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
503.855 1209.52KNm
Distance of centroid of forces from y-axis
= 2.401m
Eccentricity = 0.824m
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 9.005m 513.29KNm
2 57 9.005m 513.29KNm
3 57 7.805m 444.89KNm
4 57 7.805m 444.89KNm
5 34 3.505m 119.17KNm
6 34 3.505m 119.17KNm
7 34 0.505m 17.17KNm
8 34 0.505m 17.17KNm
9 21.06KN 4.690m 98.78KNm
10 118.79KN 4.690m 557.14KNm
503.855 2844.94KN
Distance of centroid of forces from x-axis
= 5.646m
Eccentricity = 0.956m
Y
X5500
8000
Location of Resultant
2524
5574
Calculation of reactions on abutments:-
299.41KN
204.44KN
Hence,the critical reaction is Ra = 299.4KN
The corrected reaction at obtuse corner = 299.41KN
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 =
Y
X5500
8000
Location of Resultant
2524
5574
300
300
185
815815
740
The eccentricty of the line of action of live load at bottom of abutment = 0.815m
----do----on top of 1st footing = 0.815m
----do----on top of 2nd footing = 0.740m
The eccentricity in the other direction need not be considered due to high section modulus in transverse direction.
3.Impact of vehicles:-
As per Clause 211 of IRC:6--2000,impact allowance shall be made by an increment
of live load by a factor 4.5/(6+L)
Hence,the factor is 0.353
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 0.1765
For the remaining portion,impact need not be considered.
4.Wind load:-
The deck system is located at height of (RTL-LBL) 2.10m
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 = 1.790
Breadth of the deck system = 7.38
The effective area exposed to wind force =HeightxBreadth =
Kg/m2.
300
300
185
815815
740
Hence,the wind force acting at centroid of the deck system = 3.91KN(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 strip footing = 4.79m
5.Water current force:-
Water pressure considered on square ended abutments as per clause 213.2 of IRC:6---2000 is
24.18
(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 = 0.51KN
Point of action of water current force from the top of RCC raft footing = 2.90m
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
50.39KN
The location of the tractive force from the top of RCC raft footing = 4.49m
7.Buoyancy :-
As per clause 216.4 of IRC:6---2000,for abutments or piers of shallow depth,the
P = 52KV2 = Kg/m2.
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 = 13.34Cum
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
21.18Cum
Reduction in self wieght = 211.80KN
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*(54.04+30)/180] = 0.961Sin(a-q) = SIN[3.14*(54.04-15)/180] = 0.875Sina = SIN[3.14*(54.04)/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*(54.04+0)/180] = 0.97
From the above expression,
0.71
The hieght of abutment above GL,as per the preliminary section assumed = 1.804m
Hence,maximum pressure at the base of the wall Pa = 23.06KN/sqm
Ka =
Ka =
The pressure distribution along the height of the wall is as given below:-
Surcharge load = 15.34 KN/sqm
15.34
1.804
23.06 15.34
Area of the rectangular portion = 27.67Area of the triangular portion = 20.8
48.47
Taking moments of the areas about the toe of the wall
S.No Description Area Lever arm Moment
1 Rectangular 27.67 0.902 24.958342 Triangular 20.80 0.60133333 12.50773333
48.47 37.46607333
Height from the bottom of the wall = 0.77m
The active Earth pressure acts on the abutment as shown below:-
0.70
50.961.804m
0.77m
54.04
2.000.56
Total earth pressure acting on the abutment P = 266.60KN
168.01KN
206.99KN
Eccentricity of vertical component of earth pressure = 0.44m
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 1.48m
2.40
BFL -0.92m
Horizontal component of the earth pressure Ph =
Vertical component of the earth pressure Pv =
24.00kn/sqm
Total horizontal water pressure force = 158.40KN
The above pressure acts at height of H/3 = 0.80m
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 322.90KN -0.740 0.00
2 Self wieght of abutment&footings 508.38KN 0.115 0.000
3 405.10KN -0.740 0.000
4 Impact load 0.00 0.00 0.00
1236.38
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.79
2 Tractive,Braking&Frictional resistance of bearings 50.39KN y-Direction 4.49
3 Water current force 0.51KN x-Direction 2.90
Check for stresses:-
About x-axis:-
Breadth of 2nd footing b = 6.25m
Depth of 2nd footing d = 2.45m
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)
Area of the footing = A = 15.3125
Section modulus of bottom footing 6.25
about x-axis --Zx =
i.e, 4000KN/sqm
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN -0.740 6.112 Self wieght of abutment&footings 508.38KN 0.115 36.873 Reaction due to live load with impact factor 405.10KN -0.740 7.664 Impact load 0.00KN 0.000 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 50.39KN 4.49 -36.18
14.46
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.740 36.072 Self wieght of abutment&footings 508.38KN -0.115 29.543 Reaction due to live load with impact factor 405.10KN 0.740 45.254 Impact load 0.00KN 0.000 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 50.39KN 4.49 36.18
147.04
Stress at heel = P/A(1+6e/b)+M/Z = 14.46 KN/Sqm>-2000KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 147.04 KN/Sqm<4000KN/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 =
m2
(1/6)bd2 = m3
For M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 grade of concrete permissible tensile stress in bending tension is -2N/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
i.e, 4000KN/sqm
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 21.092 Self wieght of abutment&footings 508.38KN 0.00 33.23 Reaction due to live load with impact factor 405.10KN 0.000 26.464 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.79 -4.966 Water current force 0.51KN 2.90 -0.09
75.70
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 21.092 Self wieght of abutment&footings 508.38KN 0.00 33.23 Reaction due to live load with impact factor 405.10KN 0.000 26.464 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.79 4.966 Water current force 0.51KN 2.90 0.09
85.8
Stress at up stream side P/A(1+6e/b)+M/Z = 75.70 KN/Sqm>-2000KN/sqm.edge =
Hence safe.
Stress at down stream side P/A(1+6e/b)+M/Z = 85.8 KN/Sqm<4000KN/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
For M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 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)
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)
1 Reaction due to dead load from super structure 322.90KN -0.740 0.00
2 Self wieght of abutment&cut waters 411.36KN 0.210 0.000
3 Reaction due to live load with impact factor 405.10KN -0.740 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 4.49
2 Tractive,Braking&Frictional resistance of bearings 50.39KN y-Direction 4.19
3 Water current force 0.51KN x-Direction 2.60
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, 4000KN/sqm
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN -0.74 6.512 Self wieght of abutment&footings 411.36KN 0.21 31.123 Reaction due to live load with impact factor 405.10KN -0.74 8.164 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 50.39KN 4.19 -38.31
7.48
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.74 38.42
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 M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 grade of concrete permissible tensile stress in bending tension is -2N/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)
2 Self wieght of abutment&footings 411.36KN -0.21 22.853 Reaction due to live load with impact factor 405.10KN 0.74 48.24 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 50.39KN 4.19 38.31
147.78
Stress at heel = P/A(1+6e/b)+M/Z = 7.48 KN/Sqm>-2000KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 147.78 KN/Sqm<4000KN/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, 4000KN/sqm
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 22.462 Self wieght of abutment&footings 411.36KN 0.00 28.623 Reaction due to live load with impact factor 405.10KN 0.000 28.184 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.49 -4.956 Water current force 0.51KN 2.60 -0.09
74.22
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 22.462 Self wieght of abutment&footings 411.36KN 0.00 28.623 Reaction due to live load with impact factor 405.10KN 0.000 28.18
m2
(1/6)bd2 = m3
For M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 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)
4 Impact load 0.00KN 0.00 0Horizontal loads:- (Stress = M/Z)
5 Wind load 16.50KN 4.49 4.956 Water current force 0.51KN 2.60 0.09
84.3
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 74.22 KN/Sqm>-2000KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 84.3 KN/Sqm<4000KN/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 322.90KN -0.815 0.002 Self wieght of abutment&footings 320.28KN 0.270 0.0003 Reaction due to live load with impact factor 405.10KN -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 4.192 Tractive,Braking&Frictional resistance of bearings 50.39KN y-Direction 3.893 Water current force 0.51KN x-Direction 2.30
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, 4000KN/sqm
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 M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN -0.82 5.622 Self wieght of abutment&footings 320.28KN 0.27 28.943 Reaction due to live load with impact factor 405.10KN -0.82 7.054 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 50.39KN 3.89 -47.04
-5.43
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.82 46.042 Self wieght of abutment&footings 320.28KN -0.27 18.983 Reaction due to live load with impact factor 405.10KN 0.82 57.764 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 50.39KN 3.89 47.04
169.82
Stress at heel = P/A(1+6e/b)+M/Z = -5.43 KN/Sqm>-2000KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 169.82 KN/Sqm<4000KN/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, 4000KN/sqm
i.e, -2000KN/sqm
For M15 grade of concrete permissible tensile stress in bending tension is -2N/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 M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 grade of concrete permissible tensile stress in bending tension is -2N/mm2
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 25.832 Self wieght of abutment&footings 320.28KN 0.00 25.623 Reaction due to live load with impact factor 405.10KN 0.000 32.414 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.19 -5.316 Water current force 0.51KN 2.30 -0.09
78.46
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 25.832 Self wieght of abutment&footings 320.28KN 0.00 25.623 Reaction due to live load with impact factor 405.10KN 0.000 32.414 Impact load 0.00KN 0.00 0
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.19 5.316 Water current force 0.51KN 2.30 0.09
89.26
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 78.46 KN/Sqm>-2000KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 89.26 KN/Sqm<4000KN/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 322.90KN -0.740 0.00
Self wieght of abutment&cut waters 508.38KN
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)
Reduction in self weight due to buoyancy -211.80KN
2 Net self weight 296.58KN 0.115 0.000
3 Vertical component of earth pressure 206.99KN 0.440 0.000
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.79
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Water current force 0.51KN x-Direction 2.90
4 Horizontal load due to earth pressure 168.01KN y-Direction 1.37
5 Water pressure force 158.40KN y-Direction 0.80
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, 4000KN/sqm
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN -0.74 6.112 Net self wieght of abutment&footings 296.58KN 0.11 21.513 Vertical component of Earth pressure 206.99KN 0.44 19.23
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 168.01KN 1.37 -36.895 Water pressure force 158.40KN 0.80 20.3
30.23
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.74 36.072 Net self wieght of abutment&footings 296.58KN -0.11 17.233 Vertical component of Earth pressure 206.99KN -0.44 7.81
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 M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 grade of concrete permissible tensile stress in bending tension is -2N/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)
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 168.01KN 1.37 36.895 Water pressure force 158.40KN 0.80 -20.3
77.73
Stress at heel = P/A(1+6e/b)+M/Z = 30.22 KN/Sqm>-2000KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 77.73 KN/Sqm<4000KN/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, 4000KN/sqm
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 21.092 Net self wieght of abutment&footings 296.58KN 0.00 19.373 Vertical component of Earth pressure 206.99KN 0.00 13.52
Horizontal loads:- (Stress = M/Z)4 Wind load 16.50KN 4.79 -4.965 Water current force 0.51KN 2.90 -0.1
48.93
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 21.092 Net self wieght of abutment&footings 296.58KN 0.00 19.373 Vertical component of Earth pressure 206.99KN 0.00 13.52
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 4.79 4.965 Water pressure force 0.51KN 2.90 0.1
59.03
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 48.93 KN/Sqm>-2000KN/sqm.
m2
(1/6)bd2 = m3
For M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 grade of concrete permissible tensile stress in bending tension is -2N/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)
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 59.03 KN/Sqm<4000KN/sqm
Hence safe.
ii)On top of 2nd footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 322.90KN -0.74 0.00
Self wieght of abutment&footings 508.38KN
Reduction in self weight due to buoyancy -211.80KN
2 Net self weight 296.58KN 0.115 0.000
3 Vertical component of earth pressure 206.99KN 0.440 0.000
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.49
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Water current force 0.51KN x-Direction 2.60
4 Horizontal load due to earth pressure 168.01KN y-Direction 1.07
5 Water pressure force 158.40KN y-Direction 0.50
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 =
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 M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
i.e, 4000KN/sqm
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN -0.74 6.512 Net self wieght of abutment&footings 296.58KN 0.11 22.913 Vertical component of Earth pressure 206.99KN 0.44 20.48
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 168.01KN 1.07 -32.725 Water pressure force 158.40KN 0.50 14.4
31.55
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.74 38.422 Net self wieght of abutment&footings 296.58KN -0.11 18.353 Vertical component of Earth pressure 206.99KN -0.44 8.32
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 168.01KN 1.07 32.725 Water pressure force 158.40KN 0.50 -14.4
83.44
Stress at heel = P/A(1+6e/b)+M/Z = 31.55 KN/Sqm>-2000KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 83.44 KN/Sqm<4000KN/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, 4000KN/sqm
i.e, -2000KN/sqm
For M15 grade of concrete permissible tensile stress in bending tension is -2N/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 M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 grade of concrete permissible tensile stress in bending tension is -2N/mm2
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 22.462 Net self wieght of abutment&footings 296.58KN 0.00 20.633 Vertical component of Earth pressure 206.99KN 0.00 14.4
Horizontal loads:- (Stress = M/Z)4 Wind load 16.50KN 4.49 -4.955 Water current force 0.51KN 2.60 -0.1
52.45
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 22.462 Net self wieght of abutment&footings 296.58KN 0.00 20.633 Vertical component of Earth pressure 206.99KN 0.00 14.4
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 4.49 4.955 Water pressure force 0.51KN 2.60 0.1
62.53
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 52.45 KN/Sqm>-2000KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 62.53 KN/Sqm<4000KN/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 322.90KN -0.74 0.00
Self wieght of abutment&cut waters 411.36KN
Reduction in self weight due to buoyancy -171.40KN
2 Net self weight 239.96KN 0.210 0.000
3 Vertical component of earth pressure 206.99KN 0.440 0.000
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)
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 4.19
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Water current force 0.51KN x-Direction 2.30
4 Horizontal load due to earth pressure 168.01KN y-Direction 0.77
5 Water pressure force 158.40KN y-Direction 0.20
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, 4000KN/sqm
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN -0.74 6.512 Net self wieght of abutment&footings 239.96KN 0.21 20.063 Vertical component of Earth pressure 206.99KN 0.44 20.48
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 168.01KN 0.77 -23.575 Water pressure force 158.40KN 0.20 5.8
29.23
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.74 38.422 Net self wieght of abutment&footings 239.96KN -0.21 13.333 Vertical component of Earth pressure 206.99KN -0.44 8.32
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 168.01KN 0.77 23.575 Water pressure force 158.40KN 0.20 -5.8
77.89
Stress at heel = P/A(1+6e/b)+M/Z = 29.23 KN/Sqm>-2000KN/sqm.
Intensity in KN
Location(Ht.from the section considered).(m)
m2
(1/6)bd2 = m3
For M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 grade of concrete permissible tensile stress in bending tension is -2N/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 = 77.89 KN/Sqm<4000KN/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, 4000KN/sqm
i.e, -2000KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 22.462 Net self wieght of abutment&footings 239.96KN 0.00 16.693 Vertical component of Earth pressure 206.99KN 0.00 14.4
Horizontal loads:- (Stress = M/Z)4 Wind load 16.50KN 4.19 -4.625 Water current force 0.51KN 2.30 -0.1
48.85
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 322.90KN 0.00 22.462 Net self wieght of abutment&footings 239.96KN 0.00 16.693 Vertical component of Earth pressure 206.99KN 0.00 14.4
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 4.19 4.625 Water pressure force 0.51KN 2.30 0.1
58.25
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 48.85 KN/Sqm>-2000KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 58.25 KN/Sqm<4000KN/sqm
m2
(1/6)bd2 = m3
For M15 grade of concrete permissible compressive stress in direct compreession is 4N/mm2
For M15 grade of concrete permissible tensile stress in bending tension is -2N/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)
Hence safe.
V)Check for stability of abutments:-
a)Load Envelope-III:-(The Canal is dry,back fill intact with live load on span)
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 322.90KN 0.82 0.00
2 Self wieght of abutments 320.23KN 0.270 0.000
3 Reaction due to live load with impact factor 405.10KN 0.82 0.000
4 Vertical component of Active Earth pressure 206.99KN 0.440 0.00
1255.22KN
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.19
2 Tractive,Braking&Frictional resistance of bearings 50.39KN y-Direction 4.19
3 Horizontal Active Earth pressure force 168.01KN y-Direction 0.77
234.90KN
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 = 211.12Kn-m
Moment due to active earth pressure force = 129.87Kn-m
Total overturning moment = 340.99Kn-m
Taking moments of all the restoring forces about toe of the abutment wrt x-axis,,
Moment due to self weight of abutment = 406.69Kn-m
Moment due to live load reaction on abutment = 735.27Kn-m
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)
Moment due to super structure load reaction on abutment = 586.05Kn-m
Moment due to vertical component of active earth pressure = 298.07Kn-m
Total Restoring moment = 2026.08Kn-m
Factor of safety = 5.94180648 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)
Check for stability against sliding:-
1255.22KN
234.90KN
Coefficient of friction between concrete surfaces = 0.80
4.27491751 > 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 322.90KN 0.82 0.00
Self wieght of abutments 320.23KN
-133.40KN
2 Net self wieght 186.83KN 0.270 0.000
3 Vertical component of Active Earth pressure 206.99 0.440 0.00
S.No Type of load Direction x or y
1 Wind load 16.50KN x-Direction 4.19
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
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)
3 Active Earth pressure force 168.01KN y-Direction 0.77
4 Force due to water pressure 158.40KN y-Direction 0.20
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 = 129.87Kn-m
Total overturning moment = 129.87Kn-m
Taking moments of all the restoring forces about toe of the abutment wrt x-axis,
Moment due to self weight of abutment = 237.27Kn-m
Moment due to water pressure force on the abutment = 31.68Kn-m
Moment due to super structure load reaction on abutment = 586.05Kn-m
Moment due to vertical component of active earth pressure = 298.07Kn-m
Total Restoring moment = 1153.08Kn-m
Factor of safety = 8.87855106 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)
Check for stability against sliding:-
552.22KN
168.01KN
Coefficient of friction between concrete surfaces = 0.80
2.62940787 > 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 Vemuladeevi Channel
Abutment
Abutment
Length of the Raft:- = 12.60m
Width of the Raft:- = 6.55m
Total load on the Raft:-
Dead Load:-
Wt.of Deck slab = 477.28Kn
Wt.of wearing coat = 69.51Kn
Wt.of bed blocks over abutments = 99.00Kn
Wt.of abutments
Footing-I = 182.16KnFooting-II = 194.04KnWt.of abutments = 640.46Kn
Total 1662.45Kn
Dead load stress = 20.14Kn/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 6.8
1.2 4.3 3.0 3.0 0.475
0.625
12.60m
Centre of gravity of loading from 1st 11.4t load =
= 4.33m
Centre of gravity from the end of raft = 4.955m
Eccentricity = 1.345m
Stress due to live load = 1xP(1+6e/b)(Taking single lanes) A
Max.stress = 11.45Kn/Sqm
Min.stress = -0.78Kn/Sqm
Total stress due to dead load and live load
Max.Stress = 31.59Kn/Sqm
Min.Stress = 19.36Kn/Sqm
Assuming the depth of raft as 60cm
Stress due to self weight of raft = 15.00Kn/Sqm
Stress due to wieght of base concrete = 7.20Kn/Sqm
Hence,the Max.stress on the soil = 53.79Kn/Sqm
Which is less than 6t/sqm(Soil testing report)
Hence safe.
Net Max.upward pressure acting on Raft = 31.59Kn/Sqm
Net Min.upward pressure acting on Raft = 19.36Kn/Sqm
The design stress = 25.48Kn/Sqm
Hence,the UDL on the raft = 25.48Kn/m
Design of Raft:-
The raft will be analysed as a continuous beam of 1m width with the loadingas shown below:-
1.30 10.00 1.30
UDL of 25.48Kn/m
After analysis the bending moment diagram is as given below:
517
37.5
Max.Negative bending moment Mu = 517.00KNm
Max.Positive bending moment Mu = 37.50KNm
Effective depth required d = 387.11mm
Over all depth provided = 600.00mm
Effective depth provided(Assuming 40mm cover) d = 542.00mm
Bottom steel:-
1.76
From table 3 of SP 16,percentage of steel required = 0.535
Area of steel required = 2899.70sqmm
Top steel:-
0.128
From table 3 of SP 16,percentage of steel required/Minimum steel = 0.12
Area of steel required = 650.40sqmm
Hence provide 12mm dia HYSD bars@ 150mm c/c spacing at bottom and provide 20mm bars at 110mm c/c at top
2854.55sqmm
753.60sqmm
Provide distribution reinforcement of 0.12% both at top and bottom
Area = 720.00sqmm
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 = 157.00mm
Hence provide 12mm dia bars @ 150mm c/c spacing at top& bottom
Effective depth = 300-50-6 = 0.244m
Clear span between abutments = 3.00-2x(0.125+2x(0.15)) = 2.150m
Effective span = 2.15+0.244/2 = 2.27m
For continuous slab,clear span will be the effective span,effective span =
The raft is proposed to be designed for the Max.stress of 5.47t/sqm
Assuming 1m width of raft,the UDL on the raft is 53.790t/Sqm
The raft is treated as simply supported beam with over hangs
34.71t-m
2.42t-m
Max.negative moment = 2.420t-m
Max.positive moment = 34.710t-m
Hence,the Max.positive moment = wl2/8 =
Max.Negative moment for over hangs = wl12/2 =
Hence,the design moment = 34.710t-m
67.140094 7.7x100
Hence provide overall depth of 30cm,the effective depth available is
300-50-6 = 24.4
77.65sqcm at centre 2000x0.916x24.4
Spacing of 12mm dia bars required = 1.13x100/7.9 = 14.303797468
However provide 12mm bars at 125mm c/c at centre
5.41sqcm for over hangs 2000x0.916x24.4
Spacing of 12mm dia bars required = 1.13x100/0.56 = 201.78571429
However provide 12mm bars at 250mm c/c
Provide distribution reinforcement of 0.12% both at top and bottom
Area = 3.60sqcm
Adopting 10mm dia bars,the spacing required is = 0.785x100/3.6 = 21.805556
Hence provide 10mm dia bars @ 175mm c/c spacing
The details of Reinforcement is as shown below:-
12mm bars@ 125 c/c(Curtail 50% of cranks at the centre of abutment
3.00m
12mm bars@250mm c/c
Depth required = 3.53x105
Area of steel required = 3.53x105
Area of steel required = 0.25x105
DESIGN OF RAFT FOR THE SLAB CULVERT
0.625 11.41.2 11.44.3 6.8
3 6.83 6.8
0.475
2.27m
1.1304
1.1304
0.785
12mm bars@250mm c/c
Hydraulic design
Hydraulic Particulars:-
1.Full supply Level 1.477
2.Ordinary Flood level ------
3.Lowest Bed level 0.477
4.Average bed slope 0.000059(1 in 17000)
0.020(As per table 5 of IRC:SP 13)
6.Vertical clearence proposed 0.510(As per clause 15.5 of IRC:SP 13&as per profile)
6.Bottom of deck proposed 1.987(MFL+Vertical clearence)
7.Road Crest level 2.577(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 = 2.074Cumecs
2)Area Velocity method:-
Depth of flow w.r.t HFL = 1.000m
Bed width = 4.50m
Assuming side slopes 1:1.5 in clayey soils,top width at HFL = 6.000m
Wetted Area = 5.25sqm
Wetted perimetre = 7.33m
Hydraulic Radius R= Total area/Wetted perimeter = 0.72
Velocity V = 0.31m/sec
Discharge Q = AXV 1.63Cumecs
Design Discharge = 2.074Cumecs
Design Velocity = 0.31m/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.
6.91m
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 = 0.05m6.00m
Clear span = 6.00mEffective linear water way = 6.00m
Depth of flow = 1.00m
Head due to velocity of approach = 0.004m
Combined head due to Velocity of approach and 0.054mafflux
0.93m/sec
Linear water way required 2.24m
No.of vents required = = 0.3733333333333Say---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= 1(6/6.00)
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*2.0740.5 =
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 65 KN/m2 at a depth of 1.50m below LBL
Hence open foundation in the form of raft is proposed at a depth of 1.85m 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
2.76Cumecs
1.00
0.46
0.80m
1.20m
2.40m
-0.923m
1.400m
-0.923m