design of 4m span rcc slab culvert
DESCRIPTION
Design of RCC Slab culvertTRANSCRIPT
Construction of 4.00mts span culvert
Name of the work:-R/f R&B Road to Sariapalli SC colony
Construction of 4.00mts span culvert
Name of the work:-R/f R&B Road to Sariapalli SC colony
Design Philosophy:-
The design of 1V-- 4.37m right span culvert is carried as per the procedure out lined
below:-
Step1:-
The design discharge was fixed after arriving discharge based on the following methods:-
and area by considering actual cross-section of the channel.
Step2:-
The vertical clearence and afflux are verified.
below the maximum scour depth
Step3:-
The structural components are desined in the following manner:-
and culverts of medium importance is selected.
designed as per the guide lines given in relevent IRC codes.
a.As per the hydraulic particulars furnished by the Irrigation department
b.By Area-Velocity method using Manning's equation for arriving at the flow velocity
a.Hydraulic particulars like HFL,OFL are obtained from Irrigation department.
b.Bottom of deck level was fixed based on HFL and road formation levels on both sides.
c.Ventway calculations are done for fixation of ventway.
d.Normal scour depth with reference to HFL was calculated using Lacey's equations
e.After arriving at the Maximum scour depth,bottom level of the foundation was fixed
After arriving at bottom of deck level,bottom of foundation level and required ventway,the dimensions of the bridge are finalised.
a.As per the recommendations of IRC 6:2000,IRC class A live load required for bridges
b.Load combination is selected as per IRC 6:2000
c.Based on the trial pit particulars and soil test reports,type of foundation was selected.
d.The structural components like Abutment,raft foundation are
e.The deck slab is proposed as per the MOST drawing Nos.BD 1-74&BD 2-74
f.The dirt wall is proposed as per the drawings given in Plate No.7.25 of IRC:SP20-2002(Rural roads manual)
Design of Abutments
I)Design Parameters:-
Clear Right Span = 4.00m
= 4.740m
Width of the carriage way = 5.50m
= 0.395m
= 0.075m
= 1.200m
Thickness of dirt wall = 0.30m
Sectional area of dirt wall = 0.330sqm
Thickness of RAFT footing = 0.40m
Height of abutments = 1.650m
(As per hydralic calculations)
Top width of abutments = 0.690m
Bottom width of abutments = 1.20m
Sectional area of abutment section = 1.559sqm
Bank side batter of abutment = 0.510m
Stream side batter of abutment = 0.000m
Width of 1st footing = 1.50m
Thickness of 1st footing = 0.30m
= 0.15m
Bank side offset of 1st footing wrt abutment = 0.15m
= 1.65m
= 0.30m
= 0.30m
Bank side offset of 2nd footing wrt abutment = 0.15m
Width of 3rd footing = 0.00m
Thickness of 3rd footing = 0.00m
Canal side offset of 3rd footing wrt abutment = 0.00m
Bank side offset of 3rd footing wrt abutment = 0.00m
Width of VRCC RAFT footing = 6.75m
= 0.40m
Type of bearings = No bearings proposed
Deck slab length
Thickness of deck slab as per MOST Dg.BD 1-74
Thickness of wearing coat
Height of railing
Canal side offset of 1st footing wrt abutment
Width of 2nd footing
Thickness of 2nd footing
Canal side offset of 2nd footing wrt abutment
Thickness of VRCC RAFT footing
= 25KN/cum
= 24KN/cum
= 18KN/Cum
= 10KN/Cum
= 30
= 72.86
= 0
= 15
= 1.20m
= 2.605m
= 0.785m
= 1.705m
= -0.815m
= 6.50t/sqm
= 25.00N/sqmm
= 415.00N/sqmm
Cover to reinforcement = 50.00mm
II)General loading pattern:-
As per IRC:6---2000,the following loadings are to be considered on the bridge or slabculvert:-
1.Dead load2.Live load3.Impact load4.Wind load5.Water current6.Tractive,braking effort of vehicles&frictional resistance of bearings7.Buoyancy8.Earth pressure9.Seismic force10.Water pressure force
As per clause 202.3,the increase in permissible stresses is not permissible for theabove loading combination.
III)Loading on the slab culvert for design of abutments:-
1.Dead Load:-
i)Self wieght of the deck slab = 128.72KN
Unit weight of RCC (yrc
)
Unit weight of PCC (ypc
)
Density of back fill soil behind abutments (y)
Unit weight of water (yw)
Angle of shearing resistance of back fill material(Q)
Angle of face of wall supporting earth with horizontal(In degrees)(in clock wise direction)(a)
Slope of back fill (b)
Angle of wall friction (q)
Height of surcharge considered (h3)
Road crest level (RTL)
Low bed level (LBL)
High flood Level (HFL)Bottom of foundation level (BFL) Safe Bearing Capacity of the soil (SBC)
Compressive strength of concrete for RCC Raft footing (f
ck)
Yield strength of steel (fy)
ii)Self wieght of dirtwall over abutment = 45.38KN
iii)Self weight of wearing coat = 24.44KN
198.54KN
There is no need to consider snow load as per the climatic conditions
Self wieght of the abutments upto bottom most footing based on the preliminary section assumed:-
iv)Self wieght of the abutment section = 205.79KN
v)Self wieght of top footing = 59.40KN
vi)Self wieght of 2nd footing = 65.34KN
vii)Self wieght of 3rd footing = 0.00KN
viii)Self wieght of 4th footing = 0.00KN
330.53KN
ix)Calculation of eccentricity of self weight of abutment w.r.t base of abutment
W1W1
S.No Description Load in KN
1 55.539 0.86
2 150.282 0.345
3 0 0
205.821
Location of resultant from toe of abutment = 0.48m
Eccentricity wrt centre of base of abutment = 0.120m
x)Calculation of eccentricity of self weight of abutment&1st footing w.r.t bottom of 1st footing
S.No Description Load in KN
1 Back batter 55.539 1.01
2 Centre portion 150.282 0.495
3 Front batter 0 0
4 1st footing 59.40KN 0.75
265.221
Location of resultant from toe of abutment = 0.66m
Eccentricity wrt centre of 1st footing= 0.090m
xi)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 2nd footing
Distance of centroid of load from toe of abutment
Back batter(W1)
Centre portion(W2)
Front batter(W3)
Distance of centroid of load from toe of 1st footing
S.No Description Load in KN
1 Back batter 55.539 1.16
2 Centre portion 150.282 0.645
3 Front batter 0 0.3
4 1st footing 59.40KN 0.900
5 2nd footing 65.34KN 0.825
330.561
Location of resultant from toe of abutment = 0.81m
Eccentricity = 0.015m
xii)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 3rd footing
S.No Description Load in KN
1 Back batter 0 1.162 Centre portion 0 0.6453 Front batter 0 0.34 1st footing 0 0.605 2nd footing 0 0.536 3rd footing 0 0.00
0
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
Distance of centroid of load from toe of 2nd footing
Distance of centroid of load from toe of 3rd footing
GENERAL IRC Class-A loading Pattern
are to be designed for IRC Class A loading.2.
7t
2.7
t
11.4
t
11.4
t
6.8
t
6.8t
6.8
t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
clauses 207.1.3&207.4
The ground contact area of wheels for the above placement,each axle wise isgiven below:-
Axle load Ground Contact Area(Tonnes) B(mm) W(mm)
11.4 250 5006.8 200 3802.7 150 200
Assuming 0.475m allowance for guide posts/kerbs and the clear distance of vehicle from
the edge of guide post being 0.15m as per clause 207.1,the value of 'f' shown in the figure will
be 0.625m
0.625m
3.525m
4.15m
The IRC Class A loading as per the drawing is severe and the same is to be considered as per
Hence,the width of area to be loaded with 5KN/m2 on left side is (f) =
Similarly,the area to be loaded on right side (k) =
Y
X
11.4t
11.4t
475
5500
Portion to be loadedwith 5KN/m² liveload
5380
35252925
4000
6052.7t
The total live load on the deck slab composes the following components:-
1.Wheel loads----Point loads
2.Live load in remaing portion(Left side)----UDL
2.Live load in remaing portion(Right side)----UDL
Resultant live load:-
Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)
Taking moments of all the forces w.r.t y-axis
S.No Distance from Y-axis
1 57 0.875m
2 57 0.875m
3 57 2.675m
4 57 2.675m
5 13.5 0.875m
6 13.5 2.675m
7 14.8125 0.313m
8 83.5425 4.688m
353.355
Distance of centroid of forces from y-axis
= 2.402m
Eccentricity = 0.823m
Eccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)
Taking moments of all the forces w.r.t x-axis
Wheel Load/UDL in KN
S.No Load in KN Distance from X-axis
1 57 5.005m
2 57 5.005m
3 57 3.805m
4 57 3.805m
5 13.5 0.605m
6 13.5 0.605m
7 14.81KN 2.690m
8 83.54KN 2.690m
353.355
Distance of centroid of forces from x-axis
= 3.637m
Eccentricity = 0.947m
Y
X
Location of Resultant
3637
2402
Calculation of reactions on abutments:-
238.88KN
114.48KN
Hence,the critical reaction is Ra = 238.88KN
The corrected reaction at obtuse corner = 238.88KN
Assuming that the live load reaction acts at the centre of the contact area on the abutment,
The eccentricty of the line of action of live load at bottom of abutment = 0.415m
----do----on top of 1st footing = 0.415m
----do----on top of 2nd footing = 0.340m
The eccentricity in the other direction need not be considered due to high section modulus in transverse direction.
Reaction due to loads Ra =
Reaction due to point loads = Rb =
Y
X
Location of Resultant
3637
2402
300
300
205
415
415
340
3.Impact of vehicles:-
As per Clause 211 of IRC:6--2000,impact allowance shall be made by an increment
of live load by a factor 4.5/(6+L)
Hence,the factor is 0.419
Further as per clause 211.7 of IRC:6--2000,the above impact factor shall be only
50% for calculation of pressure on piers and abutments just below the level of bed block.There
is no need to increase the live load below 3m depth.
As such,the impact allowance for the top 3m of abutments will be
For the remaining portion,impact need not be considered.
4.Wind load:-
The deck system is located at height of (RTL-LBL) 1.82m
The Wind pressure acting on deck system located at that height is considered for design.
As per clause 212.3 and from Table .4 of IRC:6---2000,the wind pressure at that hieght is=
59.48
Height of the deck system = 1.670
Breadth of the deck system = 5.34
The effective area exposed to wind force =HeightxBreadth =
Hence,the wind force acting at centroid of the deck system =(Taking 50% perforations)
Further as per clause 212.4 of IRC:6---2000 ,300 Kg/m wind force is considered to be
acting at a hieght of 1.5m from road surface on live load vehicle.
Hence,the wind force acting at 1.5m above the road surface =
The location of the wind force from the top of RCC raft footing =
Kg/m2.
5.Water current force:-
Water pressure considered on square ended abutments as per clause 213.2 of IRC:6---2000 is
17.94
(where the value of 'K' is 1.5 for square ended abutments)
For the purpose of calculation of exposed area to water current force,only 1.0m
width of abutment is considered for full hieght upto HFL
Hence,the water current force = 0.33KN
Point of action of water current force from the top of RCC raft footing =
6.Tractive,braking effort of vehicles&frictional resistance of bearings:-
The breaking effect of vehicles shall be 20% of live load acting in longitudinal
direction at 1.2m above road surface as per the clause 214.2 of IRC:6--2000.
As no bearings are assumed in the present case,50% of the above longitudinal
force can be assumed to be transmitted to the supports of simply supported spans resting on
stiff foundation with no bearings as per clause 214.5.1.3 of IRC:6---2000
Hence,the longitudinal force due to braking,tractive or frictional resistance of
bearings transferred to abutments is
35.34KN
The location of the tractive force from the top of RCC raft footing =
7.Buoyancy :-
As per clause 216.4 of IRC:6---2000,for abutments or piers of shallow depth,the dead weight of the abutment shall be reduced by wieght of equal volume of water upto HFL.
The above reduction in self wieght will be considered assuming that the back fill behind the abutment is scoured.
For the preliminary section assumed,the volume of abutment section is
P = 52KV2 = Kg/m2.
i)Volume of abutment section = 8.57Cum
ii)Volume of top footing = 2.48Cum
iii)Volume of 2nd footing = 2.72Cum
iv)Volume of 3rd footing = 0.00Cum
v)Volume of 4th footing = 0.00Cum
13.77Cum
Reduction in self wieght = 137.72KN
8.Earth pressure :-
As per clause 217.1 of IRC:6---2000,the abutments are to be designed for a
surcharge equivalent to a back fill of hieght 1.20m behind the abutment.
The coefficient of active earth pressure exerted by the cohesion less back fill on
the abutment as per the Coulomb's theory is given by
'2Sin(a+Q)
sina sin(a-q) sin(Q+q)sin(Q-b)
sin(a+b)
Sin(a+Q) = SIN[3.14*(72.86+30)/180] = 0.975Sin(a-q) = SIN[3.14*(72.86-15)/180] = 0.846Sina = SIN[3.14*(72.86)/180] = 0.955Sin(Q+q) = SIN[3.14*(30+15)/180] = 0.707Sin(Q-b) = SIN[3.14*(30-0)/180] = 0.5Sin(a+b) = SIN[3.14*(72.86+0)/180] = 0.955
From the above expression,
0.45
The hieght of abutment above GL,as per the preliminary section assumed =
Hence,maximum pressure at the base of the wall Pa =
The pressure distribution along the height of the wall is as given below:-
Ka =
Ka =
Surcharge load = 9.72 KN/sqm
9.72
1.650
13.37 9.72
Area of the rectangular portion = 16.04Area of the triangular portion = 11.03
27.07
Taking moments of the areas about the toe of the wall
S.No Description Area Lever arm Moment
1 Rectangular 16.04 0.825 13.2332 Triangular 11.03 0.55 6.0665
27.07 19.2995
Height from the bottom of the wall = 0.71m
The active Earth pressure acts on the abutment as shown below:-
0.70
32.141.650m
0.71m
72.86
1.200.22
Total earth pressure acting on the abutment P = 148.88KN
Eccentricity of vertical component of earth pressure =
9.Siesmic force :-
As per clause 222.1 of IRC:6---2000,the bridges in siesmic zones I and II need not be
designed for siesmic forces.The location of the slab culvert is in Zone-I.Hence,there is no need to
design the bridge for siesmic forces.
10.Water pressure force:-
The water pressure distribution on the abutment is as given below:-
HFL 1.705m
2.52
Horizontal component of the earth pressure Ph =
Vertical component of the earth pressure Pv =
BFL -0.815m
25.20kn/sqm
Total horizontal water pressure force = 174.64KN
The above pressure acts at height of H/3 = 0.84m
IV)Check for stresses for abutments&footings:-
a)Load Envelope-I:-(The Canal is dry,back fill scoured with live load on span)
i)On top of RCC raft
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load Intensity in KN
1 Reaction due to dead load from super structure 198.54KN -0.340
2 Self wieght of abutment&footings 330.56KN 0.015
3 338.96KN -0.340
4 Impact load 0.00 0.00
868.07
S.No Type of load Intensity in KN Direction x or y
1 Wind load 16.50KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 35.34KN y-Direction
3 Water current force 0.33KN x-Direction
Check for stresses:-
About x-axis:-
Breadth of 2nd footing b = 6.45m
Depth of 2nd footing d = 1.65m
Area of the footing = A = 10.6425
Vertical forces acting on the abutment (P) composes of the following components
Eccentricty about x-axis(m)
Reaction due to live load with impact factor---(Wheel loads+UDL)
Horizontal forces acting/transferred on the abutment (H) composes of the following components
m2
Section modulus of bottom footing 2.93
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN -0.3402 Self wieght of abutment&footings 330.56KN 0.0153 Reaction due to live load with impact factor 338.96KN -0.3404 Impact load 0.00KN 0.000
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 35.34KN 4.22
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.3402 Self wieght of abutment&footings 330.56KN -0.0153 Reaction due to live load with impact factor 338.96KN 0.3404 Impact load 0.00KN 0.000
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 35.34KN 4.22
Stress at heel = P/A(1+6e/b)+M/Z = 15.08 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 148.06 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 3rd footing b = 1.65m
Depth of 3rd footing d = 6.45m
Area of the footing = A = 10.6425
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
m2
Section modulus of bottom footing about = 11.44
y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Self wieght of abutment&footings 330.56KN 0.003 Reaction due to live load with impact factor 338.96KN 0.0004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.526 Water current force 0.33KN 3.02
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Self wieght of abutment&footings 330.56KN 0.003 Reaction due to live load with impact factor 338.96KN 0.0004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.526 Water current force 0.33KN 3.02
Stress at up stream side P/A(1+6e/b)+M/Z = 74.96 KN/Sqm>-2800KN/sqm.edge =
Hence safe.
Stress at down stream side P/A(1+6e/b)+M/Z = 88.18 KN/Sqm<5000KN/sqmedge =
Hence safe.
i)On top of 2nd footing
The following co-ordinates are assumed:-
(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
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
Eccentricity/Lever arm
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load Intensity in KN
1 Reaction due to dead load from super structure 198.54KN -0.340
2 Self wieght of abutment&cut waters 265.22KN 0.090
3 Reaction due to live load with impact factor 338.96KN -0.340
4 Impact load 0.00 0.000
S.No Type of load Intensity in KN Direction x or y
1 Wind load 16.50KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 35.34KN y-Direction
3 Water current force 0.33KN x-Direction
Check for stresses:-
About x-axis:-
Breadth of 1st footing b = 6.45mDepth of 1st footing d = 1.50mArea of the footing = A = 9.675
Section modulus of base of abutment 2.42
about x-axis--Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)
Vertical load acting on the abutment (P) composes of the following components
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
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
1 Reaction due to dead load from super structure 198.54KN -0.342 Self wieght of abutment&footings 265.22KN 0.093 Reaction due to live load with impact factor 338.96KN -0.344 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 35.34KN 3.92
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.342 Self wieght of abutment&footings 265.22KN -0.093 Reaction due to live load with impact factor 338.96KN 0.344 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 35.34KN 3.92
Stress at heel = P/A(1+6e/b)+M/Z = 9.65 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 155.52 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 1.50mDepth of 1st footing d = 6.45mArea of the footing = A = 9.675
Section modulus of base of abutment 10.40
about y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
Intensity in KN (P)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 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 198.54KN 0.002 Self wieght of abutment&footings 265.22KN 0.003 Reaction due to live load with impact factor 338.96KN 0.0004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.226 Water current force 0.33KN 2.72
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Self wieght of abutment&footings 265.22KN 0.003 Reaction due to live load with impact factor 338.96KN 0.0004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 4.226 Water current force 0.33KN 2.72
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 76.19 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 89.75 KN/Sqm<5000KN/sqm
Hence safe.
i)On top of 1st footing
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 Intensity in KN
1 Reaction due to dead load from super structure 198.54KN -0.4152 Self wieght of abutment&footings 205.82KN 0.120
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
Eccentricity/Lever arm
Vertical load acting on the abutment (P) composes of the following components
Eccentricty about x-axis(m)
3 Reaction due to live load with impact factor 338.96KN -0.415
4 Impact load 0.00 0.000
S.No Type of load Intensity in KN Direction x or y
1 Wind load 16.50KN x-Direction2 Tractive,Braking&Frictional resistance of bearings 35.34KN y-Direction3 Water current force 0.33KN x-Direction
Check for stresses:-
About x-axis:-
Breadth of abutment b = 6.45mDepth of abutment d = 1.20mArea of the footing = A = 7.74
Section modulus of base of abutment 1.55
about x-axis--Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN -0.4152 Self wieght of abutment&footings 205.82KN 0.1203 Reaction due to live load with impact factor 338.96KN -0.4154 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 35.34KN 3.62
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.4152 Self wieght of abutment&footings 205.82KN -0.120
Horizontal load acting/transferred on the abutment (H) composes of the following components
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
Intensity in KN (P)
3 Reaction due to live load with impact factor 338.96KN 0.4154 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 35.34KN 3.62
Stress at heel = P/A(1+6e/b)+M/Z = -10.92 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 202.5 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of abutment b = 1.20mDepth of abutment d = 6.45mArea of the footing = A = 7.74
Section modulus of base of abutment 8.32
about y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Self wieght of abutment&footings 205.82KN 0.003 Reaction due to live load with impact factor 338.96KN 0.0004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 3.926 Water current force 0.33KN 2.42
S.No Type of load
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
Intensity in KN (P)
Eccentricity/Lever arm
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Self wieght of abutment&footings 205.82KN 0.003 Reaction due to live load with impact factor 338.96KN 0.0004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 16.50KN 3.926 Water current force 0.33KN 2.42
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 88.16 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 103.9 KN/Sqm<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 Intensity in KN
1 Reaction due to dead load from super structure 198.54KN -0.340
Self wieght of abutment&cut waters 330.56KN
Reduction in self weight due to buoyancy -137.72KN
2 Net self weight 192.84KN 0.015
3 Vertical component of earth pressure 79.17KN 0.380
S.No Type of load Intensity in KN Direction x or y
1 Wind load 16.50KN x-Direction
Vertical load acting on the abutment (P) composes of the following components
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction
3 Water current force 0.33KN x-Direction
4 Horizontal load due to earth pressure 126.09KN y-Direction
5 Water pressure force 174.64KN y-Direction
Check for stresses:-
About x-axis:-
Breadth of bottom footing b = 6.45mDepth of bottom footing d = 1.65mArea of the footing = A = 10.6425
Section modulus of bottom footing 2.93
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN -0.342 Net self wieght of abutment&footings 192.84KN 0.013 Vertical component of Earth pressure 79.17KN 0.38
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 126.09KN 1.315 Water pressure force 174.64KN 0.84
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.342 Net self wieght of abutment&footings 192.84KN -0.013 Vertical component of Earth pressure 79.17KN -0.38
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 126.09KN 1.315 Water pressure force 174.64KN 0.84
Stress at heel = P/A(1+6e/b)+M/Z = 34.76 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 -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 53.68 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of bottom footing b = 1.65mDepth of bottom footing d = 6.45mArea of the footing = A = 10.6425
Section modulus of bottom footing 11.44
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Net self wieght of abutment&footings 192.84KN 0.003 Vertical component of Earth pressure 79.17KN 0.00
Horizontal loads:- (Stress = M/Z)4 Wind load 16.50KN 4.525 Water current force 0.33KN 3.02
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Net self wieght of abutment&footings 192.84KN 0.003 Vertical component of Earth pressure 79.17KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 4.525 Water pressure force 0.33KN 3.02
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 37.61 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 -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 50.83 KN/Sqm<5000KN/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 Intensity in KN
1 Reaction due to dead load from super structure 198.54KN -0.34
Self wieght of abutment&footings 330.56KN
Reduction in self weight due to buoyancy -137.72KN
2 Net self weight 192.84KN 0.015
3 Vertical component of earth pressure 79.17KN 0.380
S.No Type of load Intensity in KN Direction x or y
1 Wind load 16.50KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction
3 Water current force 0.33KN x-Direction
4 Horizontal load due to earth pressure 126.09KN y-Direction
5 Water pressure force 174.64KN y-Direction
Check for stresses:-
About x-axis:-
Breadth of 2nd footing b = 6.45mDepth of 2nd footing d = 1.50mArea of the footing = A = 9.675
Vertical load acting on the abutment (P) composes of the following components
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
m2
Section modulus of bottom footing 2.42
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN -0.342 Net self wieght of abutment&footings 192.84KN 0.013 Vertical component of Earth pressure 79.17KN 0.38
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 126.09KN 1.015 Water pressure force 174.64KN 0.54
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.342 Net self wieght of abutment&footings 192.84KN -0.013 Vertical component of Earth pressure 79.17KN -0.38
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 126.09KN 1.015 Water pressure force 174.64KN 0.54
Stress at heel = P/A(1+6e/b)+M/Z = 31.51 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 65.76 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 1.50mDepth of 1st footing d = 6.45mArea of the footing = A = 9.675
Section modulus of bottom footing 10.40
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
m2
(1/6)bd2 = m3
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Net self wieght of abutment&footings 192.84KN 0.003 Vertical component of Earth pressure 79.17KN 0.00
Horizontal loads:- (Stress = M/Z)4 Wind load 16.50KN 4.225 Water current force 0.33KN 2.72
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Net self wieght of abutment&footings 192.84KN 0.003 Vertical component of Earth pressure 79.17KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 4.225 Water pressure force 0.33KN 2.72
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 41.85 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 55.41 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
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
S.No Type of load Intensity in KN
1 Reaction due to dead load from super structure 198.54KN -0.34
Self wieght of abutment&cut waters 265.22KN
Reduction in self weight due to buoyancy -110.51KN
2 Net self weight 154.71KN 0.090
3 Vertical component of earth pressure 79.17KN 0.380
S.No Type of load Intensity in KN Direction x or y
1 Wind load 16.50KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction
3 Water current force 0.33KN x-Direction
4 Horizontal load due to earth pressure 126.09KN y-Direction
5 Water pressure force 174.64KN y-Direction
Check for stresses:-
About x-axis:-
Breadth of 1st footing b = 6.45mDepth of 1st footing d = 1.20mArea of the footing = A = 7.74
Section modulus of bottom footing 1.55
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN -0.34
Vertical load acting on the abutment (P) composes of the following components
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
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
2 Net self wieght of abutment&footings 154.71KN 0.093 Vertical component of Earth pressure 79.17KN 0.38
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 126.09KN 0.715 Water pressure force 174.64KN 0.24
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.342 Net self wieght of abutment&footings 154.71KN -0.093 Vertical component of Earth pressure 79.17KN -0.38
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 126.09KN 0.715 Water pressure force 174.64KN 0.24
Stress at heel = P/A(1+6e/b)+M/Z = 22.05 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 89.68 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 1.20mDepth of 1st footing d = 6.45mArea of the footing = A = 7.74
Section modulus of bottom footing 8.32
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Net self wieght of abutment&footings 154.71KN 0.00
Intensity in KN (P)
m2
(1/6)bd2 = m3
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
3 Vertical component of Earth pressure 79.17KN 0.00Horizontal loads:- (Stress = M/Z)
4 Wind load 16.50KN 3.925 Water current force 0.33KN 2.42
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 198.54KN 0.002 Net self wieght of abutment&footings 154.71KN 0.003 Vertical component of Earth pressure 79.17KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 16.50KN 3.925 Water pressure force 0.33KN 2.42
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 48 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 63.74 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
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load Intensity in KN
1 Reaction due to dead load from super structure 198.54KN 0.415
2 Self wieght of abutments 205.79KN 0.120
3 Reaction due to live load with impact factor 338.96KN 0.415
4 Vertical component of Active Earth pressure 79.17KN 0.380
822.46KN
Intensity in KN (P)
Vertical load acting on the abutment (P) composes of the following components
Eccentricty about x-axis(m)
S.No Type of load Intensity in KN Direction x or y
1 Wind load 16.50KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 35.34KN y-Direction
3 Horizontal Active Earth pressure force 126.09KN y-Direction
177.92KN
Check for stability against over turning:-
Taking moments of all the overturning forces about toe of the abutment wrt x-axis,
Moment due to tractive,braking&frictional resistance of bearings =
Moment due to active earth pressure force =
Total overturning moment =
Taking moments of all the restoring forces about toe of the abutment wrt x-axis,,
Moment due to self weight of abutment =
Moment due to live load reaction on abutment =
Moment due to super structure load reaction on abutment =
Moment due to vertical component of active earth pressure =
Total Restoring moment =
Factor of safety = 3.376949592 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)
Check for stability against sliding:-
Coefficient of friction between concrete surfaces =
Horizontal load acting/transferred on the abutment (H) composes of the following components
Total vertical load acting on the base of the abutment Vb =
Total sliding force,ie,horizontal load on the abutment Hb =
3.698071786 > 1.5 Hence safe
(As per clause 706.3.4 of IRC:78-2000)
b)Load Envelope-IV:-(The Canal is running upto HFL with no live load on span)
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load Intensity in KN
1 Reaction due to dead load from super structure 198.54KN 0.415
Self wieght of abutments 205.79KN
-85.70KN
2 Net self wieght 120.09KN 0.120
3 Vertical component of Active Earth pressure 79.17 0.380
S.No Type of load Intensity in KN Direction x or y
1 Wind load 16.50KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction
3 Active Earth pressure force 126.09KN y-Direction
4 Force due to water pressure 174.64KN y-Direction
Check for stability against over turning:-
Taking moments of all the overturning forces about toe of the abutment wrt x-axis,
Moment due to tractive,braking&frictional resistance of bearings =
Moment due to active earth pressure force =
Total overturning moment =
Factor of safety against sliding Fs =
Vertical load acting on the abutment (P) composes of the following components
Eccentricty about x-axis(m)
Reduction in self weight due to buoyancy
Horizontal load acting/transferred on the abutment (H) composes of the following components
Taking moments of all the restoring forces about toe of the abutment wrt x-axis,
Moment due to self weight of abutment =
Moment due to water pressure force on the abutment =
Moment due to super structure load reaction on abutment =
Moment due to vertical component of active earth pressure =
Total Restoring moment =
Factor of safety = 4.532980823 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)
Check for stability against sliding:-
Coefficient of friction between concrete surfaces =
2.372288897 > 1.5 Hence safe
(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 Abutments
No bearings proposed
Moment
47.76
51.85
0
99.61
Moment
56.09
74.39
0
44.55
175.03
Moment
64.43
96.93
0
53.46
53.91
268.73
Moment
0000000
2.7t
2.7
t
11.4
t
11.4
t
6.8
t
6.8t
6.8
t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
is severe and the same is to be considered as per
Y
X
11.4t
11.4t
475
5500
Portion to be loadedwith 5KN/m² liveload
5380
35252925
4000
6052.7t
255.00KN
14.81KN
83.54KN
353.36KN
Moment
49.88KNm
49.88KNm
152.48KNm
152.48KNm
11.81KNm
36.11KNm
4.63KNm
391.61KNm
848.86KNm
Moment
285.29KNm
285.29KNm
216.89KNm
216.89KNm
8.17KNm
8.17KNm
39.85KNm
224.73KNm
1285.25KN
Y
X
Location of Resultant
3637
2402
The eccentricity in the other direction need not be considered due to high section modulus in transverse
Y
X
Location of Resultant
3637
2402
0.2095
2.65KN
16.50KN
4.52m
3.02m
4.22m
1.650m
13.37KN/sqm
126.09KN
79.17KN
0.38m
0.00
0.000
0.000
0.00
4.52
4.22
3.02
Eccentricty about y-axis(m)
composes of the following components
Location(Ht.from the section considered).(m)
12.7631.4921.78
0
-50.95
15.08
24.5630.6341.92
0
50.95
148.06
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at heelP/A(1+6e/b)
Stress at toeP/A(1+6e/b)
18.6631.0631.85
0
-6.52-0.09
74.96
18.6631.0631.85
0
6.520.09
88.18
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at upstream edgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
0.00
0.000
0.000
0.00
4.22
3.92
2.72
Eccentricty about y-axis(m)
composes of the following components
Location(Ht.from the section considered).(m)
Stress at heelP/A(1+6e/b)
14.0328.9423.95
0
-57.27
9.65
27.0125.1246.12
0
57.27
155.52
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at toeP/A(1+6e/b)
20.5227.4135.04
0
-6.69-0.09
76.19
20.5227.4135.04
0
6.690.09
89.75
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
0.000.000
Stress at upstream edgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
Eccentricty about y-axis(m)
0.000
0.00
3.923.622.42
15.7529.0726.89
0
-82.63
-10.92
35.5523.62
composes of the following components
Location(Ht.from the section considered).(m)
Stress at heelP/A(1+6e/b)
Stress at toeP/A(1+6e/b)
60.70
82.63
202.5
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
25.6526.5943.79
0
-7.77-0.1
88.16
Stress at upstream edgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
25.6526.5943.79
0
7.770.1
103.9
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
0.00
0.000
0.000
4.52
Eccentricty about y-axis(m)
composes of the following components
Location(Ht.from the section considered).(m)
0.00
3.02
1.31
0.84
12.7618.3710.07
-56.5650.1
34.76
24.5617.874.81
56.56-50.153.68
KN/Sqm>-2800KN/sqm.
Stress at heelP/A(1+6e/b)
Stress at toeP/A(1+6e/b)
KN/Sqm<5000KN/sqm
18.6618.127.44
-6.52-0.1
37.61
18.6618.127.44
6.520.1
50.83
KN/Sqm>-2800KN/sqm.
Stress at U/S EdgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
KN/Sqm<5000KN/sqm
0.00
0.000
0.000
4.22
0.00
2.72
1.01
0.54
Eccentricty about y-axis(m)
composes of the following components
Location(Ht.from the section considered).(m)
14.0320.2111.08
-52.839.0
31.51
27.0119.655.29
52.8-39.065.76
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at heelP/A(1+6e/b)
Stress at toeP/A(1+6e/b)
20.5219.938.18
-6.69-0.1
41.85
20.5219.938.18
6.690.1
55.41
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at U/S EdgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
0.00
0.000
0.000
3.92
0.00
2.42
0.71
0.24
17.54
Eccentricty about y-axis(m)
composes of the following components
Location(Ht.from the section considered).(m)
Stress at heelP/A(1+6e/b)
21.6613.84
-58.0727.1
22.05
33.7618.326.61
58.07-27.189.68
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
25.6519.99
Stress at toeP/A(1+6e/b)
Stress at U/S EdgeP/A(1+6e/b)
10.23
-7.77-0.148
25.6519.9910.23
7.770.1
63.74
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
0.00
0.000
0.000
0.00
Stress at D/S edgeP/A(1+6e/b)
Eccentricty about y-axis(m)
3.92
3.92
0.71
138.52Kn-m
89.89Kn-m
228.41Kn-m
148.17Kn-m
344.05Kn-m
201.52Kn-m
77.58Kn-m
771.32Kn-m
(As per clause 706.3.4 of IRC:78-2000)
822.46KN
177.92KN
0.80
composes of the following components
Location(Ht.from the section considered).(m)
(As per clause 706.3.4 of IRC:78-2000)
0.00
0.000
0.00
3.92
0.00
0.71
0.24
0.00Kn-m
89.89Kn-m
89.89Kn-m
Eccentricty about y-axis(m)
composes of the following components
Location(Ht.from the section considered).(m)
86.46Kn-m
41.91Kn-m
201.52Kn-m
77.58Kn-m
407.48Kn-m
(As per clause 706.3.4 of IRC:78-2000)
373.89KN
126.09KN
0.80
(As per clause 706.3.4 of IRC:78-2000)
DESIGN OF RAFT FOR THE SLAB CULVERT
Abutment
Abutment
Length of the Raft:- = 7.00m
Width of the Raft:- = 6.75m
Total load on the Raft:-
Dead Load:-
Wt.of Deck slab = 257.44Kn
Wt.of wearing coat = 48.88Kn
Wt.of bed blocks over abutments = 90.76Kn
Wt.of abutments
Footing-I = 118.80KnFooting-II = 130.68KnWt.of abutments = 411.58Kn
Total 1058.14Kn
Dead load stress = 22.39Kn/Sqm
Live Load:-
Taking IRC Class-A loading
Wheel width in the direction of movement =0.2+0.2+0.25/2 = 0.625m
11.4 11.4 2.7
Name of the work:-Construction of Slab culvert on the R/f R&B Road to Sariapalli SC colony
1.2 3.2 1.925
0.625
7.00m
Centre of gravity of loading from 1st 11.4t load =
= 1.00m
Centre of gravity from the end of raft = 1.625m
Eccentricity = 1.875m
Stress due to live load = 1xP(1+6e/b)(Taking single lanes) A
Max.stress = 20.13Kn/Sqm
Min.stress = -5.03Kn/Sqm
Total stress due to dead load and live load
Max.Stress = 42.52Kn/Sqm
Min.Stress = 17.36Kn/Sqm
Assuming the depth of raft as 40cm
Stress due to self weight of raft = 10.00Kn/Sqm
Stress due to wieght of base concrete = 7.20Kn/Sqm
Hence,the Max.stress on the soil = 59.72Kn/Sqm
Which is less than 6.5t/sqm(Soil testing report)
Hence safe.
Net Max.upward pressure acting on Raft = 42.52Kn/Sqm
Net Min.upward pressure acting on Raft = 17.36Kn/Sqm
The design stress = 29.94Kn/Sqm
Hence,the UDL on the raft = 29.94Kn/m
Design of Raft:-
The raft will be analysed as a continuous beam of 1m width with the loadingas shown below:-
0.975 5.05 0.975
UDL of 29.94Kn/m
After analysis the bending moment diagram is as given below:
115
20.2
Max.Negative bending moment Mu = 115.00KNm
Max.Positive bending moment Mu = 20.20KNm
Effective depth required d = 185.97mm
Over all depth provided = 400.00mm
Effective depth provided(Assuming 40mm cover) d = 337.50mm
Top steel:-
1.01
From table 3 of SP 16,percentage of steel required = 0.245
Area of steel required = 826.88sqmm
Bottom steel:-
0.177
From table 3 of SP 16,percentage of steel required/Minimum steel = 0.15
Area of steel required = 506.25sqmm
Mu/0.133f
ckb =
Mu/bd2 =
Mu/bd2 =
Hence provide 10mm dia HYSD bars@ 125mm c/c spacing at bottom and provide 12mm bars at 100mm c/c at top
1130.40sqmm
628.00sqmm
Provide distribution reinforcement of 0.12% both at top and bottom
Area = 480.00sqmm
Adopting 10mm dia bars,the spacing required is = 163.54mm
Hence provide 10mm dia bars @ 150mm c/c spacing at top& bottom as distribution steel
Hence Ast provided at top =
Hence Ast provided at bottom =
DESIGN OF RAFT FOR THE SLAB CULVERT
Name of the work:-Construction of Slab culvert on the R/f R&B Road to Sariapalli SC colony
Hydraulic design
Hydraulic Particulars:-
1.Full supply Level 1.705
2.Ordinary Flood level
3.Lowest Bed level 0.785
4.Average bed slope 0.000067(1 in 15000)
0.025(As per table 5 of IRC:SP 13)
6.Vertical clearence proposed 0.430(As per clause 15.5 of IRC:SP 13&as per profile)
6.Bottom of deck proposed 2.135(MFL+Vertical clearence)
7.Road Crest level 2.605(Bottom of deck level+thickness of deck slab)
8.Width of carriage way 5.500
Discharge Calculations:-
1)From the data furnished by the Irrigation Department:-
Design discharge = Nil
2)Area Velocity method:-
Depth of flow w.r.t HFL = 0.920m
Bed width = 2.50m
Assuming side slopes 1:1.5 in clayey soils,top width at HFL = 3.880m
Wetted Area = 2.93sqm
Wetted perimetre = 5.10m
Hydraulic Radius R= Total area/Wetted perimeter = 0.58
Velocity V = 0.23m/sec
Discharge Q = AXV 0.68Cumecs
Design Discharge = 0.680Cumecs
5.Rugosity Coefficient(n)
1/nX(R2/3XS1/2)
Design Velocity = 0.230m/sec
Ventway Calculations(H.F.L Condition):-
Assuming the stream to be truly alluvial,the regime width is equal to linear waterway required for the drain.
3.96m
The actual top width is almost equal to the above regime width.Hence,the stream is almost truly alluvial in nature.As per IRC:SP--13,the ventway calculations for alluvial streams are as given below:-
Assuming afflux = x = 0.15m3.88m
Clear span = 4.00mEffective linear water way = 4.00m
Depth of flow = 0.92m
Head due to velocity of approach = 0.002m
Combined head due to Velocity of approach and 0.152mafflux
1.55m/sec
Linear water way required 0.48m
No.of vents required = = 0.12Say---1 Vent
In alluvial streams,the actual width of the stream should not be reduced,as it results in enhanced scour depth and expensive training works.
Hence No.of vents required as per the width of the stream at H.F.L= 0.97
No.of vents to be provided 1Nos
No.of piers = 0Nos
Scour Depth Calculations:-
As per the clause 101.1.2 of IRC:5--1985,the design discharge should be increased by 30% to ensure adequate margin of safety for foundations and protection works
Hence,the discharge for design of foundations = 1.30XDesign Discharge =
Hence,as per Lacey's silt theory,the regime width W = 4.8Q1/2 = 4.8*0.680.5 =
Width of channel at H.F.L(b+h) =
di =
(Vmax
2/2g)X[di/(d
i+x)]2
hi =
Velocity through vents Vv = 0.90X(2gh
i)1/2 =
LWW
= Qd/(V
vXd
i) =
LWW
/LC
Discharge per metre width of foundations = q =
Bottom level of foundation =
Depth of foundation below low bed level =
The Minimum Safe Bearing capacity of the soil is considered as 60 KN/m2 at a depth of 1.60m below LBL
Hence open foundation in the form of raft is proposed at a depth of 1.60m below LBL,ie,at a level of
Cut-off walls and aprons are not required from scour depth point of view
Lacey's Silt factor ' f ' = 1.76Xm1/2(For fine silt) =
Normal scour depth D = 1.34(q2/f)1/3 =
Maximum scour depth Dm = 1.5XD =
Depth of foundation = Dm + Max.of 1.2m or 1/3 Dm =
Hydraulic design
The actual top width is almost equal to the above regime width.Hence,the stream is almost truly alluvial in nature.
In alluvial streams,the actual width of the stream should not be reduced,as it results in enhanced scour
As per the clause 101.1.2 of IRC:5--1985,the design discharge should be increased by 30% to ensure adequate
0.90Cumecs
0.200
0.225
0.85m
1.28m
2.48m
-0.77m
1.555m
-0.815m
DESIGN OF FLY WINGS
Data:-
Height of Fly wing wall =Height of wall above G.L=Height of wall below G.L=Density of back fill soil&material in toe portion = Grade of concrete =Grade of steel =Ground water Table level =
(in clock wise direction)
Surcharge over the back fill in terms of height of back fill =
Permissible compressive stress in bending for M20 Concrete (c)=Permissible tensile stress in bending for Fe 415 steel (t)=Length of the wing wall proposed =
Dimensions of the Fly wing(Assumed for preliminary design):-
Thickness of wing at support =Thickness of wing at end =
Coefficient of active earth pressure by Coulomb's theory
Sin(a+Q)
sina sin(a-q) sin(Q+q)sin(Q-b)
sin(a+b)
From the above expression,
0.3
Hence,maximum pressure at the bottom of the wall Pa =
The pressure distribution along the height of the wall is as given below:-
Pressure due toSurcharge load = 324
324
2.420m
Angle of shearing resistance of back fill material&material at toe portion(Q) = Angle of face of wall supporting earth with horizontal(a)(In degrees)
Slope of back fill(b) =Angle of wall friction (q) =
Undrained Cohesion ( c) =
Ka =
Ka =
1306.80
Total Active earth pressure force = 2365.31
Height from the bottom of the wall = 0.94m
The active earth pressure acts on the wall as shown below:-
0.15
15
0.94m2.420
900.30
Design of wall :-
Factored bending moment Mu = 10709.98Kgm
Effective depth required d = 179.47mm
Over all depth provided = 300.00mm
Effective depth provided(Assuming 40mm cover) d = 252.00mm
1.687
From table 2 of SP 16,percentage of steel required = 0.421
Area of steel required = 1060.92sqmm
Hence provide 12mm dia HYSD bars@ 100mm c/c spacing
1130.40sqmm
Check for shear:-
Percentage of tension steel = 0.45
Horizontal component of the earth pressure Ph =
Vertical component of the earth pressure Pv =
Mu/0.133f
ckb =
Mu/bd2 =
Hence Ast provided =
Maximum shear force on the member = 57.12KN
Factored Design shear force = 85.68KN
0.34 N/sqmm
Hence section is safe from shear strength point of view
The design shear strength of concrete for the above steel percentage from Table 19 of IS 456 is
0.46 N/sqmm > 0.34
Hence,no shear reinforcement is required.
Provide temperature re inforcement @ 0.15%
Area required = 337.50sqmm
Provide 10mm dia @ 150mm c/c on earthen side
Provide 10mm dia @ 150mm c/c on other side in both directions
The reinforcement detailing is shown in the drawing
Check for serviceability:-
For cantilever walls,the span to effective depth ratio is 7
0.58fy x Area of cross-section of steel required Area of cross-section of steel provided
The stress level is 272.18N/sqmm
For percentage of tension steel provided is 0.45
The modification factor for ratio of span to effective depth is 1.5
Hence,the ratio is 10.5
The effective depth required = 0.24 <0.252 (Actually provided)
Nominal shear stress tv =V
u/bd =
From Fig.4 of IS:456-2000, fs =
DESIGN OF FLY WINGS
2.420m2.420m0.00m
1800Kg/CumM25
Fe500
3090
015
0.60m
25N/sqmm500N/sqmm
2.50m
0.30m0.15m
2
sin(Q+q)sin(Q-b)
1306.80Kg/sqm
2284.80Kg/m
611.88Kg/m
<2.8 N/sqmm(As per Table 20 of 1S 456)
(Actually provided)