type design of submersible causeway
DESCRIPTION
Design of submersible causeway as per IRC SP 82--2008TRANSCRIPT
DESIGN OF VENTED SUBMERSIBLE CAUSEWAY
Name of the work:-B.T to the R/f KB Road to P.Bheemavaram
Design Philosophy:-
The design of submersible Causeway is carried out as per the procedure out
lined below:-Step1:-
The design discharge was fixed after arriving discharge based on the following methods:-
method.Further the discharge from the surplus wier of the tank is also taken into account,while finalising the design discharge.The surplus wier is treated as broad-crested wier and height of fall is locally enquired.The discharge is arrived using broad crested wier formula.
Step2:-
the causeway is kept below the HFL,so that the obstruction to flow is less than 70%, when the flow is at RTL.Further,when the flow is at HFL,the obstruction to flow is kept below 30%.All the above ventway calculations are done as per IRC SP:82--2008.
calculations are carried out.
below the maximum scour depth
Step3:-
dimensions of the bridge are finalised.
The structural components are desined in the following manner:-
and culverts of medium importance is selected.
Additional live load due to silt is considered on the deck slab as per IRC SP:82--2008.
a.Discharge of the stream is arrived using area-velocity method and catchment area
a.Hydraulic particulars like HFL,OFL are fixed as per the local enquiry.
b.It is proposed to design the structure as vented submersible causeway.RTL of
c.After finalisation of design discharge,RTL and ventway calculations,afflux
d.Normal scour depth with reference to HFL was calculated using Lacey's equations
e.After arriving at the Maximum scour depth,bottom level of the foundation was fixed
After arriving at RTL,bottom of foundation level and required ventway,the
a.As per the recommendations of IRC 6:2000,IRC class A live load required for bridges
b.The effect of drag and lift is considered on the causeway as per IRC-SP:82--2008.
c.Load combinations and remaining loads are selected as per IRC 6:2000
d.Stainless steel anchor bars and VRCC thrust blocks are proposed as per
IRC SP:82--2007 to safeguard against lift and drag forces respectively.
designed as per the guide lines given in relevent IRC codes.
e.Based on the soil test reports,indivdual foundations are proposed for an SBC of 15t/m2.
f.The structural components like Abutments,piers,face walls,strip foundation are
g.The deck slab is proposed as per the drawings given in Plate No.7.09 of IRC:SP20-2002(Rural roads manual)
h.The dirt wall is proposed as per the drawings given in Plate No.7.25 of IRC:SP20-2002(Rural roads manual)
Design of Abutments for causeway
I)Design Parameters:-
Clear Right Span = 6.00m
= 6.800m
Width of the carriage way = 6.00m
Thickness of deck slab as per IRC SP 20 = 0.480m
= 0.075m
Height of guard stones = 0.750m
Thickness of dirt wall = 0.30m
Sectional area of dirt wall = 0.370sqm
Thickness of strip footing = 0.45m
Height of abutments = 1.200m
(As per hydralic calculations)
Top width of abutments = 0.750m
Bottom width of abutments = 1.05m
Sectional area of abutment section = 1.080sqm
Bank side batter of abutment = 0.000m
Stream side batter of abutment = 0.300m
Width of 1st footing = 1.35m
Thickness of 1st footing = 0.30m
= 0.15m
Bank side offset of 1st footing wrt abutment = 0.15m
= 1.50m
= 0.30m
= 0.30m
Bank side offset of 2nd footing wrt abutment = 0.15m
Width of 3rd footing = 1.65m
Thickness of 3rd footing = 0.30m
Canal side offset of 3rd footing wrt abutment = 0.45m
Bank side offset of 3rd footing wrt abutment = 0.15m
Width of VRCC strip footing = 1.95m
= 0.45m
= 0.60m
= 0.30m
Offset of top footing along width = 0.00m
Offset of 2nd footing along width = 0.00m
Offset of 3rd footing along width = 0.00m
Deck slab length
Thickness of wearing coat
Canal side offset of 1st footing wrt abutment
Width of 2nd footing
Thickness of 2nd footing
Canal side offset of 2nd footing wrt abutment
Thickness of VRCC strip footing (d3)
Canal side offset of RCC strip footing wrt abutment (s5)
Bank side offset of RCC strip footing wrt abutment (s6)
= 0.15m
Type of bearings = No bearings proposed
= 25KN/cum
= 24KN/cum
= 18KN/Cum
= 10KN/Cum
= 30
= 90
= 0
= 15
= 1.20m
= 5.645m
= 3.965m
= 6.235m
= 2.315m
= 15.00t/sqm
= 20.00N/sqmm
= 25.00N/sqmm
= 415.00N/sqmm
Cover to reinforcement = 50.00mm
II)General loading pattern:-
As per IRC:6---2000,the following loadings are to be considered on the submersible bridge or slabculvert:-
1.Dead load2.Live load3.Impact load4.Wind load5.Water current6.Tractive,braking effort of vehicles&frictional resistance of bearings7.Buoyancy8.Earth pressure9.Seismic force10.Water pressure force
Apart from the above forces,the following pressures are to be considered as per clause 7.11.2.2 of IRC SP:82---2007:-
(a) Pressure due to static head due to afflux on upstream side and trough of standing wave on down stream side:
(b) Pressure due to velocity head
(c) Pressure due to eddies
Offset of RCC strip footing along width (w1)
Unit weight of RCC (yrc)
Unit weight of PCC (ypc)
Density of back fill soil behind abutments (y)
Unit weight of water (yw)
Angle of shearing resistance of back fill material(Q)
Angle of face of wall supporting earth with horizontal(In degrees)(in clock wise direction)(a)
Slope of back fill (b)
Angle of wall friction (q)
Height of surcharge considered (h3)
Road crest level (RTL)
Low bed level (LBL)
High flood Level (HFL)Bottom of foundation level (BFL) Safe Bearing Capacity of the soil (SBC)
Compressive strength of concrete for PCC (fck)
Compressive strength of concrete for VRCC (fck)
Yield strength of steel (fy)
(d) Pressure due to friction of water against piers and bottom of slab
(e) Force due to uplift under superstructure
super structure should also be considered:
As per clause 202.3 of IRC 6:2000,the increase in permissible stresses is not permissible for theabove loading combination.
III)Loading on the submersible bridge for design of abutments:-
1.Dead Load:-
i)Self wieght of the deck slab = 244.80KN
ii)Self wieght of dirtwall over abutment = 55.50KN
iii)Self weight of wearing coat = 38.25KN
338.55KN
There is no need to consider snow load as per the climatic conditions
Self wieght of the abutments upto bottom most footing based on the preliminary section assumed:-
iv)Self wieght of the abutment section = 155.52KN
v)Self wieght of top footing = 58.32KN
vi)Self wieght of 2nd footing = 64.80KN
vii)Self wieght of 3rd footing = 71.28KN
viii)Self wieght of 4th footing = 0.00KN
349.92KN
As per the clause 7.11.3.4 of IRC:SP82--2007,Additional load of 150 mm thick silt with density equal to 15 kN/m 3 spread over the entire soffit(in case of box girders) and deck slabs of all types of
W1
W2
W3
b1
b2 b1 b3
ix)Calculation of eccentricity of self weight of abutment w.r.t base of abutment
S.No Description Load in KN Moment
1 0 1.05 0
2 129.6 0.675 87.48
3 25.92 0.2 5.18
155.52 92.66
Location of resultant from toe of abutment = 0.60m
Eccentricity wrt centre of base of abutment = 0.075m
x)Calculation of eccentricity of self weight of abutment&1st footing w.r.t bottom of 1st footing
S.No Description Load in KN Moment
1 Back batter 0 1.2 0
2 Centre portion 129.6 0.825 106.92
3 Front batter 25.92 0.35 9.07
4 1st footing 58.32 0.675 39.37
213.84 155.36
Location of resultant from toe of abutment = 0.73m
Eccentricity wrt centre of 1st footing= 0.055m
Distance of centroid of load from toe of abutment
Back batter(W1)
Centre portion(W2)
Front batter(W3)
Distance of centroid of load from toe of 1st footing
W1
W2
W3
b1
b2 b1 b3
xi)Calculation of eccentricity of self weight of abutment,1st&2nd footings w.r.t bottom of 2nd footing
S.No Description Load in KN Moment
1 Back batter 0 1.35 0
2 Centre portion 129.6 0.975 126.36
3 Front batter 25.92 0.5 12.96
4 1st footing 58.32 0.83 48.11
5 2nd footing 64.8 0.75 48.6
278.64 236.03
Location of resultant from toe of abutment = 0.85m
Eccentricity = 0.100m
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 1.35 02 Centre portion 129.6 0.975 126.363 Front batter 25.92 0.5 12.964 1st footing 58.32 0.83 48.115 2nd footing 64.8 0.75 48.66 3rd footing 71.28 0.83 58.81
349.92 294.84
Location of resultant from toe of abutment = 0.84m
Eccentricity = 0.015m
2.Live Load:-
As per clause 201.1 of IRC:6--2000,the bridges and culverts of medium importance
GENERAL IRC Class-A loading Pattern
Distance of centroid of load from toe of 2nd footing
Distance of centroid of load from toe of 3rd footing
are to be designed for IRC Class A loading.
2.7t
2.7t
11.4
t
11.4
t
6.8t
6.8t
6.8t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
2.7t
2.7t
11.4
t
11.4
t
6.8t
6.8t
6.8t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
clauses 207.1.3&207.4
The ground contact area of wheels for the above placement,each axle wise isgiven below:-
Axle load Ground Contact Area(Tonnes) B(mm) W(mm)
11.4 250 5006.8 200 3802.7 150 200
Assuming 0.3m allowance for guide posts and the clear distance of vehicle from
the edge of guide post being 0.15m as per clause 207.1,the value of 'f' shown in the figure will
be 0.45m
0.45m
3.25m
3.70m
The IRC Class A loading as per the drawing is severe and the same is to be considered as per
Hence,the width of area to be loaded with 7.25KN/m2 on left side is (f) =
Similarly,the area to be loaded on right side (k) =
6800
1200
4300
11.4t
11.4t
6.8t
1800
450
2750 3250
Area to be loadedwith 5KN/m² liveload + 2.25KN/m²silt load
Y
X
The total live load on the deck slab composes the following components:-
1.Wheel loads----Point loads 296.00KN
2.Live load in remaing portion(Left side)----UDL 22.185KN
2.Live load in remaing portion(Right side)----UDL 160.225KN
478.41KN
Resultant live load:-
Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)
Taking moments of all the forces w.r.t y-axis
S.No Distance from Y-axis Moment
1 57 0.70m 39.90KNm
2 57 0.70m 39.90KNm
3 57 2.50m 142.50KNm
4 57 2.50m 142.50KNm
5 34 0.64m 21.76KNm
6 34 2.44m 82.96KNm
7 22.185 0.225m 4.99KNm
8 160.225 4.375m 700.98KNm
478.410 1175.50KNm
Distance of centroid of forces from y-axis
= 2.457m
Eccentricity = 0.543m
Eccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)
Taking moments of all the forces w.r.t x-axis
S.No Load in KN Distance from X-axis Moment
1 34 0.925m 31.45KNm
Wheel Load/UDL in KN
2 34 0.925m 31.45KNm
5 57 5.225m 297.83KNm
6 57 5.225m 297.83KNm
7 57 6.425m 366.22KNm
8 57 6.425m 366.22KNm
9 22.19KN 3.400m 75.43KNm
10 160.23KN 3.400m 544.77KNm
478.41 2011.19KN
Distance of centroid of forces from x-axis
= 4.204m
Eccentricity = 0.804m
Location of resultant is as shown below:-
Calculation of reactions on abutments:-
Y
X
6800
6000
804
542
182.64KN
295.77KN
Hence,the critical reaction is Ra = 295.77KN
The corrected reaction = 295.77KN
Assuming that the live load reaction acts at the centre of the contact area on the abutment,
The eccentricty of the line of action of live load = 0.01m
3.Impact of vehicles:-
As per Clause 211 of IRC:6--2000,impact allowance shall be made by an increment
of live load by a factor 4.5/(6+L)
Hence,the factor is 0.352
Reaction due to loads Ra =
Reaction due to point loads = Rb =
300
535 516
Further as per clause 211.7 of IRC:6--2000,the above impact factor shall be only
50% for calculation of pressure on piers and abutments just below the level of bed block.There
is no need to increase the live load below 3m depth.
As such,the impact allowance for the top 3m of abutments will be 0.176
For the remaining portion,impact need not be considered.
4.Wind load:-
The deck system is located at height of (RTL-LBL) 1.68m
The Wind pressure acting on deck system located at that height is considered for design.
As per clause 212.3 and from Table .4 of IRC:6---2000,the wind pressure at that hieght is=
59.48
Height of the deck system = 1.755
Breadth of the deck system = 7.4
The effective area exposed to wind force =HeightxBreadth =
Hence,the wind force acting at centroid of the deck system = 3.86KN(Taking 50% perforations)
Further as per clause 212.4 of IRC:6---2000 ,300 Kg/m wind force is considered to be
acting at a hieght of 1.5m from road surface on live load vehicle.
Hence,the wind force acting at 1.5m above the road surface = 18.00KN
The location of the wind force from the top of RCC strip footing = 4.16m
5.Water current force:-
a)Water current force on deck slab:-
3.65m/sec
201.24
(where the value of 'K' is 1.5 )
Force acting on centroid of deck slab = 3.80KN
Kg/m2.
Velocity of stream at top,when the flow approaches the top of deck slab = √2 x Vmean =
P = 52KV2 = Kg/m2.
Point of action of water current force from the top of RCC strip footing = 3.09m
b)Water current force on abutment:-
Water pressure is considered on square ended abutments as per clause 213.2 of
IRC:6---2000 is
For the purpose of calculation of exposed area to water current force,only 1.0m
width of abutment is considered for full hieght upto HFL
Hence,the water current force = 3.38KN
Point of action of water current force from the top of RCC strip footing = 2.88m
6.Tractive,braking effort of vehicles&frictional resistance of bearings:-
The breaking effect of vehicles shall be 20% of live load acting in longitudinal
direction at 1.2m above road surface as per the clause 214.2 of IRC:6--2000.
As no bearings are assumed in the present case,50% of the above longitudinal
force can be assumed to be transmitted to the supports of simply supported spans resting on
stiff foundation with no bearings as per clause 214.5.1.3 of IRC:6---2000
Hence,the longitudinal force due to braking,tractive or frictional resistance of
bearings transferred to abutments is
47.84KN
The location of the tractive force from the top of RCC strip footing = 3.86m
7.Buoyancy :-
As per clause 216.4 of IRC:6---2000,for abutments or piers of shallow depth,the dead weight of the abutment shall be reduced by wieght of equal volume of water upto HFL.
The above reduction in self wieght will be considered assuming that the back fill behind the abutment is scoured.
For the preliminary section assumed,the volume of abutment section is
i)Volume of abutment section = 6.48Cum
ii)Volume of top footing = 2.43Cum
iii)Volume of 2nd footing = 2.70Cum
iv)Volume of 3rd footing = 2.97Cum
v)Volume of 4th footing = 0.00Cum
14.58Cum
Reduction in self wieght = 145.80KN
8.Earth pressure :-
As per clause 217.1 of IRC:6---2000,the abutments are to be designed for a
surcharge equivalent to a back fill of hieght 1.20m behind the abutment.
The coefficient of active earth pressure exerted by the cohesion less back fill on
the abutment as per the Coulomb's theory is given by
'2Sin(a+Q)
sina sin(a-q) sin(Q+q)sin(Q-b)
sin(a+b)
Sin(a+Q) = SIN[3.14*(76.06+30)/180] = 0.961Sin(a-q) = SIN[3.14*(76.06-15)/180] = 0.875Sina = SIN[3.14*(76.06)/180] = 0.97Sin(Q+q) = SIN[3.14*(30+15)/180] = 0.707Sin(Q-b) = SIN[3.14*(30-0)/180] = 0.5Sin(a+b) = SIN[3.14*(76.06+0)/180] = 0.97
From the above expression,
0.3
The hieght of abutment above GL,as per the preliminary section assumed = 1.200m
Hence,maximum pressure at the base of the wall Pa = 6.48KN/sqm
The pressure distribution along the height of the wall is as given below:-
Surcharge load = 6.48 KN/sqm
6.48
1.200
6.48 6.48
Ka =
Ka =
Area of the rectangular portion = 7.78Area of the triangular portion = 3.89
11.67
Taking moments of the areas about the toe of the wall
S.No Description Area Lever arm Moment
1 Rectangular 7.78 0.6 4.6682 Triangular 3.89 0.4 1.556
11.67 6.224
Height from the bottom of the wall = 0.53m
The active Earth pressure acts on the abutment as shown below:-
0.70
151.200m
0.53m
90
1.050
Total earth pressure acting on the abutment P = 69.98KN
67.60KN
18.10KN
Eccentricity of vertical component of earth pressure = 0.53m
9.Siesmic force :-
As per clause 222.1 of IRC:6---2000,the bridges in siesmic zones I and II need not be
designed for siesmic forces.The location of the slab culvert is in Zone-I.Hence,there is no need to
design the bridge for siesmic forces.
10.Water pressure force:-
As per clause 7.11.2.2(b) of IRC SP82:2007,the pressure due to static head will be zero at the surface of
water and will increase linearly to P = wh at depth 'h' from the surface, below which it will be constant as indicated
in the sketch below :-
Where, w = unit weight of water
h = afflux or depth of superstructure (including wearing coat) whichever is more.
Horizontal component of the earth pressure Ph =
Vertical component of the earth pressure Pv =
555 5.55KN/m²
1125
Total horizontal water pressure force = 11.48KN
The above pressure acts at height of 0.42H = 0.71m
11.Pressure due to eddies :-
2gWhere,
V = velocity of approach(w = unit weight of water; g= Acceleration due to gravity)
Pressure force due to eddies = 0.007KN
which is negligible.Hence it need not be considered
12. Pressure due to friction of water against piers and bottom of slab :-
Where,
ρ = mass density of water (w/g)
C = value of constant generally taken as10%
i)Force due to friction on Deck slab:-
Frictional force on bottom and top of deck slab = 4.96KN
The location of the frictional force from the top of RCC strip footing = 3.09m
ii)Force due to friction on abutment:-
Frictional force on the canal side face of abutment = 0.50KN
The location of the frictional force from the top of RCC strip footing = 1.50m
13. Force due to uplift under superstructure :-
This force acts vertically upwards and is given by
Pressure due to eddies = w (Vv-V)2
Vv = velocity of flow through the vents,
Pressure due to friction =f x ρ x (Cx Vv)2
f = friction coefficient = 1
Vv = velocity of flow through the vents (m/sec)
Uplift force = wh x Asp
555 5.55KN/m²
1125
Where,
h = the uplift head under the deckslab which may be taken as higher of the following two values: (i) Afllux(ii) Thickness of superstructure including wearing coat-head loss due to increase in
following expression
2g
Where,
V = velocity of approach
Afflux = 0.131m
Head loss due to increase in velocity = 0.012m
Hence,up lift head = 0.543m
Hence uplift force on the deck slab = 195.48KN
IV)Check for stresses for abutments&footings:-
a)Load Envelope-I:-(The Canal is dry,back fill scoured with live load on span)
i)On top of RCC Strip footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 338.55KN 0.00 0.00
2 Self wieght of abutment&footings 349.92KN 0.015 0.000
3 347.83KN -0.01 0.543
4 Impact load 52.06 -0.01 0.543
1088.35
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 4.16
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction 3.86
Asp area of the superstructure in plan
velocity through vents (Vv) Head loss due to increase in velocity through the vents is calculated by
h1 = Vv2-V2
Vv =velocity of flow through the vents
Vertical forces acting on the abutment (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Reaction due to live load with impact factor---(Wheel loads+UDL)
Horizontal forces acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
3 Water current force 3.38KN x-Direction 2.88
Check for stresses:-
About x-axis:-
Breadth of 3rd footing b = 6.00m
Depth of 3rd footing d = 1.65m
Area of the footing = A = 9.9
Section modulus of bottom footing 2.72
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 34.22 Self wieght of abutment&footings 349.92KN 0.02 35.883 Reaction due to live load with impact factor 347.83KN -0.01 34.784 Impact load 52.06KN -0.01 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.86 -67.83
(Stress = -31.36*4.93/6.38)37.03
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 34.22 Self wieght of abutment&footings 349.92KN -0.02 34.823 Reaction due to live load with impact factor 347.83KN 0.01 35.494 Impact load 52.06KN -0.01 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.86 67.83
172.34
Stress at heel = P/A(1+6e/b)+M/Z = 37.03 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 172.34 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at heelP/A(1+6e/b)
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
Breadth of 3rd footing b = 1.65m
Depth of 3rd footing d = 6.00m
Area of the footing = A = 9.9
Section modulus of bottom footing about = 9.90
y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 34.22 Self wieght of abutment&footings 349.92KN 0.00 35.353 Reaction due to live load with impact factor 347.83KN -0.543 -34.244 Impact load 52.06KN 0.54 15.64
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 4.16 -7.566 Water current force 3.38KN 2.88 -0.98
42.41
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 34.22 Self wieght of abutment&footings 349.92KN 0.00 35.353 Reaction due to live load with impact factor 347.83KN 0.543 104.514 Impact load 52.06KN 0.54 15.64
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 4.16 7.566 Water current force 3.38KN 2.88 0.98
198.24
Stress at up stream side P/A(1+6e/b)+M/Z = 42.41 KN/Sqm>-2800KN/sqm.edge =
Hence safe.
Stress at down stream side P/A(1+6e/b)+M/Z = 198.24 KN/Sqm<5000KN/sqmedge =
Hence safe.
ii)On top of 3rd footing
The following co-ordinates are assumed:-
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at upstream edgeP/A(1+6e/b)
Intensity in KN (P)
Eccentricity/Lever arm
Stress at D/S edgeP/A(1+6e/b)
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 338.55KN 0.00 0.00
2 Self wieght of abutment&footings 278.64KN 0.100 0.000
3 Reaction due to live load with impact factor 347.83KN -0.01 0.543
4 Impact load 52.06 -0.01 0.543
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 3.86
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction 3.56
3 Water current force 3.38KN x-Direction 2.58
Check for stresses:-
About x-axis:-
Breadth of 2nd footing b = 6.00mDepth of 2nd footing d = 1.50mArea of the footing = A = 9
Section modulus of Ist footing about 2.25
x-axis--Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 37.622 Self wieght of abutment&footings 278.64KN 0.10 34.063 Reaction due to live load with impact factor 347.83KN -0.01 38.264 Impact load 52.06KN -0.01 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.56 -75.7
Vertical load acting on the abutment (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at heelP/A(1+6e/b)
34.24
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 37.622 Self wieght of abutment&footings 278.64KN -0.10 27.863 Reaction due to live load with impact factor 347.83KN 0.01 39.034 Impact load 52.06KN -0.01 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.56 75.7
180.21
Stress at heel = P/A(1+6e/b)+M/Z = 34.23 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 180.21 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 1.50mDepth of 1st footing d = 6.00mArea of the footing = A = 9
Section modulus of Ist footing about 9.00
y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 37.622 Self wieght of abutment&footings 278.64KN 0.00 30.963 Reaction due to live load with impact factor 347.83KN -0.543 -45.294 Impact load 52.06KN 0.54 18.35
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.86 -7.726 Water current force 3.38KN 2.58 -0.97
32.95
S.No Type of load
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at upstream edgeP/A(1+6e/b)
Intensity in KN (P)
Eccentricity/Lever arm
Stress at D/S edgeP/A(1+6e/b)
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 37.622 Self wieght of abutment&footings 278.64KN 0.00 30.963 Reaction due to live load with impact factor 347.83KN 0.543 122.594 Impact load 52.06KN 0.54 18.35
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.86 7.726 Water current force 3.38KN 2.58 0.97
218.21
Stress at up stream side P/A(1+6e/b)+M/Z = 32.95 KN/Sqm>-2800KN/sqm.edge =
Hence safe.
Stress at down stream side P/A(1+6e/b)+M/Z = 218.21 KN/Sqm<5000KN/sqmedge =
Hence safe.
i)On top of 2nd footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 338.55KN 0.00 0.00
2 Self wieght of abutment&cut waters 213.84KN 0.055 0.000
3 Reaction due to live load with impact factor 347.83KN -0.01 0.543
4 Impact load 52.06 -0.01 0.543
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 3.56
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction 3.26
3 Water current force 3.38KN x-Direction 2.28
Check for stresses:-
About x-axis:-
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)
Breadth of 1st footing b = 6.00mDepth of 1st footing d = 1.35mArea of the footing = A = 8.1
Section modulus of base of abutment 1.82
about x-axis--Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 41.82 Self wieght of abutment&footings 213.84KN 0.06 27.483 Reaction due to live load with impact factor 347.83KN -0.01 42.514 Impact load 52.06KN -0.01 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.26 -85.58
26.21
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 41.82 Self wieght of abutment&footings 213.84KN -0.06 24.953 Reaction due to live load with impact factor 347.83KN 0.01 43.374 Impact load 52.06KN -0.01 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.26 85.58
195.7
Stress at heel = P/A(1+6e/b)+M/Z = 26.21 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 195.7 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 1.35mDepth of 1st footing d = 6.00mArea of the footing = A = 8.1
Section modulus of base of abutment 8.10
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at heelP/A(1+6e/b)
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
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 338.55KN 0.00 41.82 Self wieght of abutment&footings 213.84KN 0.00 26.43 Reaction due to live load with impact factor 347.83KN -0.543 -60.694 Impact load 52.06KN 0.54 21.94
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.56 -7.916 Water current force 3.38KN 2.28 -0.95
20.59
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 41.82 Self wieght of abutment&footings 213.84KN 0.00 26.43 Reaction due to live load with impact factor 347.83KN 0.543 146.574 Impact load 52.06KN 0.54 21.94
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.56 7.916 Water current force 3.38KN 2.28 0.95
245.57
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 20.59 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 245.57 KN/Sqm<5000KN/sqm
Hence safe.
i)On top of 1st footing
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
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at upstream edgeP/A(1+6e/b)
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
S.No Type of load
1 Reaction due to dead load from super structure 338.55KN 0.00 0.002 Self wieght of abutment&footings 155.52KN 0.075 0.0003 Reaction due to live load with impact factor 347.83KN -0.01 0.543
4 Impact load 52.06 -0.01 0.543
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 3.562 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction 2.963 Water current force 3.38KN x-Direction 2.28
Check for stresses:-
About x-axis:-
Breadth of abutment b = 6.00mDepth of abutment d = 1.05mArea of the footing = A = 6.3
Section modulus of base of abutment 1.10
about x-axis--Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 53.742 Self wieght of abutment&footings 155.52KN 0.07 26.453 Reaction due to live load with impact factor 347.83KN -0.01 54.664 Impact load 52.06KN -0.01 0
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 2.96 -128.44
6.41
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 53.742 Self wieght of abutment&footings 155.52KN -0.07 22.833 Reaction due to live load with impact factor 347.83KN 0.01 55.76
Intensity in KN
Eccentricty about x-axis(m)
Eccentricty about y-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at heelP/A(1+6e/b)
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
4 Impact load 52.06KN -0.01 0Horizontal loads:- (Stress = M/Z)
5 Tractive,Braking&Frictional resistance of bearings 47.84KN 2.96 128.44
260.77
Stress at heel = P/A(1+6e/b)+M/Z = 6.41 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 260.77 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of abutment b = 1.05mDepth of abutment d = 6.00mArea of the footing = A = 6.3
Section modulus of base of abutment 6.30
about y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 53.742 Self wieght of abutment&footings 155.52KN 0.00 24.693 Reaction due to live load with impact factor 347.83KN -0.543 25.234 Impact load 52.06KN 0.54 33.9
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.56 -10.176 Water current force 3.38KN 2.28 -1.22
126.17
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 53.742 Self wieght of abutment&footings 155.52KN 0.00 24.693 Reaction due to live load with impact factor 347.83KN 0.543 226.524 Impact load 52.06KN 0.54 33.9
Horizontal loads:- (Stress = M/Z)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at upstream edgeP/A(1+6e/b)
Intensity in KN (P)
Eccentricity/Lever arm
Stress at D/S edgeP/A(1+6e/b)
5 Wind load 18.00KN 3.56 10.176 Water current force 3.38KN 2.28 1.22
350.24
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 126.17 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 350.24 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 Strip footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 338.55KNDeduct uplift pressure -195.48KNNet reaction due to dead load from super structure 143.07KN 0.00 0.00
Self wieght of abutment&cut waters 349.92KN
Reduction in self weight due to buoyancy -145.80KN
2 Net self weight 204.12KN 0.015 0.000
3 Vertical component of earth pressure 18.10KN 0.525 0.000
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 4.16
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Water current force on deck slab 3.80KN x-Direction 3.09
4 Water current force on abutment 3.38KN x-Direction 2.88
5 Frictional force due to water on deck slab 4.96KN x-Direction 3.09
6 Frictional force due to water on abutment 0.50KN x-Direction 1.50
7 Horizontal load due to earth pressure 67.60KN y-Direction 1.43
8 Water pressure force 11.48KN y-Direction 1.61
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)
Check for stresses:-
About x-axis:-
Breadth of bottom footing b = 6.00mDepth of bottom footing d = 1.65mArea of the footing = A = 9.9
Section modulus of bottom footing 2.72
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 14.452 Net self wieght of abutment&footings 204.12KN 0.015 20.933 Vertical component of Earth pressure 18.10KN 0.53 2.79
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 1.43 -35.595 Water pressure force 11.48KN 1.61 6.8
9.34999999999999
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 14.452 Net self wieght of abutment&footings 204.12KN -0.02 20.313 Vertical component of Earth pressure 18.10KN -0.53 0.87
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 1.43 35.595 Water pressure force 11.48KN 1.61 -6.8
64.45
Stress at heel = P/A(1+6e/b)+M/Z = 9.35 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 64.45 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of bottom footing b = 1.65mDepth of bottom footing d = 6.00mArea of the footing = A = 9.9
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at heelP/A(1+6e/b)
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
m2
Section modulus of bottom footing 9.90
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 14.452 Net self wieght of abutment&footings 204.12KN 0.00 20.623 Vertical component of Earth pressure 18.10KN 0.00 1.83
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 4.16 -7.565 Water current force on abutment 3.38KN 2.88 -1.06 Water current force on deck slab 3.80KN 3.09 -1.27 Frictional force due to water on deck slab 4.96KN 3.09 -1.68 Frictional force due to water on abutment 0.50KN 1.50 -0.1
25.54
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 14.452 Net self wieght of abutment&footings 204.12KN 0.00 20.623 Vertical component of Earth pressure 18.10KN 0.00 1.83
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 4.16 7.565 Water current force on abutment 3.38KN 2.88 1.06 Water current force on deck slab 3.80KN 3.09 1.27 Frictional force due to water on deck slab 4.96KN 3.09 1.68 Frictional force due to water on abutment 0.50KN 1.50 0.1
48.26
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 25.54 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 48.26 KN/Sqm<5000KN/sqm
Hence safe.
ii)On top of 3rd footing
The following co-ordinates are assumed:-
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at U/S EdgeP/A(1+6e/b)
Intensity in KN (P)
Stress at D/S edgeP/A(1+6e/b)
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 338.55KNDeduct uplift pressure -195.48KNNet reaction due to dead load from super structure 143.07KN 0.00 0.00
Self wieght of abutment&footings 278.64KN
Reduction in self weight due to buoyancy -116.10KN
2 Net self weight 162.54KN 0.100 0.000
3 Vertical component of earth pressure 18.10KN 0.525 0.000
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 3.86
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Water current force on deck slab 3.80KN x-Direction 2.79
4 Water current force on abutment 3.38KN x-Direction 2.58
5 Frictional force due to water on deck slab 4.96KN x-Direction 2.79
6 Frictional force due to water on abutment 0.50KN x-Direction 1.20
7 Horizontal load due to earth pressure 67.60KN y-Direction 1.13
8 Water pressure force 11.48KN y-Direction 1.31
Check for stresses:-
About x-axis:-
Breadth of 2nd footing b = 6.00mDepth of 2nd footing d = 1.50mArea of the footing = A = 9
Section modulus of bottom footing 2.25
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/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 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
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 15.92 Net self wieght of abutment&footings 162.54KN 0.10 19.873 Vertical component of Earth pressure 18.10KN 0.53 3.07
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 1.13 -34.055 Water pressure force 11.48KN 1.31 6.7
11.45
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 15.92 Net self wieght of abutment&footings 162.54KN -0.10 16.253 Vertical component of Earth pressure 18.10KN -0.53 0.96
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 1.13 34.055 Water pressure force 11.48KN 1.31 -6.7
60.5
Stress at heel = P/A(1+6e/b)+M/Z = 11.45 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 60.5 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 1.50mDepth of 1st footing d = 6.00mArea of the footing = A = 9
Section modulus of bottom footing 9.00
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 15.92 Net self wieght of abutment&footings 162.54KN 0.00 18.06
Intensity in KN (P)
Eccentricity/Lever arm
Stress at heelP/A(1+6e/b)
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at U/S EdgeP/A(1+6e/b)
3 Vertical component of Earth pressure 18.10KN 0.00 2.01Horizontal loads:- (Stress = M/Z)
4 Wind load 18.00KN 3.86 -7.725 Water current force on deck slab 3.80KN 2.79 -1.26 Water current force on abutment 3.38KN 2.58 -1.07 Frictional force due to water on deck slab 4.96KN 2.79 -1.58 Frictional force due to water on abutment 0.50KN 1.20 -0.1
24.49
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 15.92 Net self wieght of abutment&footings 162.54KN 0.00 18.063 Vertical component of Earth pressure 18.10KN 0.00 2.01
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.86 7.725 Water current force on deck slab 3.80KN 2.79 1.26 Water current force on abutment 3.38KN 2.58 1.07 Frictional force due to water on deck slab 4.96KN 2.79 1.58 Frictional force due to water on abutment 0.50KN 1.20 0.1
47.45
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 24.49 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 47.45 KN/Sqm<5000KN/sqm
Hence safe.
iii)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 338.55KNDeduct uplift pressure -195.48KNNet reaction due to dead load from super structure 143.07KN 0.00 0.00
Self wieght of abutment&cut waters 213.84KN
Reduction in self weight due to buoyancy -89.10KN
2 Net self weight 124.74KN 0.055 0.000
3 Vertical component of earth pressure 18.10KN 0.525 0.000
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)
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 3.56
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Water current force on deck slab 3.80KN x-Direction 2.49
4 Water current force on abutment 3.38KN x-Direction 2.28
5 Frictional force due to water on deck slab 4.96KN x-Direction 2.49
6 Frictional force due to water on abutment 0.50KN x-Direction 0.90
7 Horizontal load due to earth pressure 67.60KN y-Direction 0.83
8 Water pressure force 11.48KN y-Direction 1.01
Check for stresses:-
About x-axis:-
Breadth of 1st footing b = 6.00mDepth of 1st footing d = 1.35mArea of the footing = A = 8.1
Section modulus of bottom footing 1.82
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 17.662 Net self wieght of abutment&footings 124.74KN 0.06 16.253 Vertical component of Earth pressure 18.10KN 0.53 3.41
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 0.83 -30.915 Water pressure force 11.48KN 1.01 6.3
12.74
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 17.662 Net self wieght of abutment&footings 124.74KN -0.06 14.553 Vertical component of Earth pressure 18.10KN -0.53 1.06
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at heelP/A(1+6e/b)
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 0.83 30.915 Water pressure force 11.48KN 1.01 -6.3
57.85
Stress at heel = P/A(1+6e/b)+M/Z = 12.74 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 57.85 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 1.35mDepth of 1st footing d = 6.00mArea of the footing = A = 8.1
Section modulus of bottom footing 8.10
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 17.662 Net self wieght of abutment&footings 124.74KN 0.00 15.43 Vertical component of Earth pressure 18.10KN 0.00 2.23
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.56 -7.915 Water current force on deck slab 3.80KN 2.49 -1.26 Water current force on abutment 3.38KN 2.28 -1.07 Frictional force due to water on deck slab 4.96KN 2.49 -1.58 Frictional force due to water on abutment 0.50KN 0.90 -0.1
23.68
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 17.662 Net self wieght of abutment&footings 124.74KN 0.00 15.43 Vertical component of Earth pressure 18.10KN 0.00 2.23
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.56 7.915 Water current force on deck slab 3.80KN 2.49 1.2
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at U/S EdgeP/A(1+6e/b)
Intensity in KN (P)
Stress at D/S edgeP/A(1+6e/b)
6 Water current force on abutment 3.38KN 2.28 1.07 Frictional force due to water on deck slab 4.96KN 2.49 1.58 Frictional force due to water on abutment 0.50KN 0.90 0.1
46.9
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 23.68 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 46.9 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 vehiclesb)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 338.55KNDeduct uplift pressure -195.48KNNet reaction due to dead load from super structure 143.07KN 0.00 0.00Self wieght of abutment&cut waters 213.84KNReduction in self weight due to buoyancy -89.10KN
2 Net self weight 124.74KN 0.055 0.0003 Vertical component of earth pressure 18.10KN 0.525 0.000
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 3.262 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.003 Water current force on deck slab 3.80KN x-Direction 2.194 Water current force on abutment 3.38KN x-Direction 1.985 Frictional force due to water on deck slab 4.96KN x-Direction 2.196 Frictional force due to water on abutment 0.50KN x-Direction 0.607 Horizontal load due to earth pressure 67.60KN y-Direction 0.538 Water pressure force 11.48KN y-Direction 0.71
Check for stresses:-
About x-axis:-
Breadth of abutment b = 6.00mDepth of abutment d = 1.05mArea of the footing = A = 6.3
Section modulus of bottom footing 1.10
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
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 22.712 Net self wieght of abutment&footings 124.74KN 0.06 20.893 Vertical component of Earth pressure 18.10KN 0.53 4.38
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 0.53 -32.75 Water pressure force 11.48KN 0.71 7.4
22.63
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 22.712 Net self wieght of abutment&footings 124.74KN -0.06 18.713 Vertical component of Earth pressure 18.10KN -0.53 1.36
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 67.60KN 0.53 32.75 Water pressure force 11.48KN 0.71 -7.4
68.13
Stress at heel = P/A(1+6e/b)+M/Z = 22.63 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 68.13 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of abutment b = 1.05mDepth of abutment d = 6.00mArea of the footing = A = 6.3
Section modulus of bottom footing 6.30
about y-axis --Zy =
i.e, 5000KN/sqm
For M20 grade of concrete permissible compressive stress in direct compreession is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Stress at heelP/A(1+6e/b)
Intensity in KN (P)
Stress at toeP/A(1+6e/b)
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
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 22.712 Net self wieght of abutment&footings 124.74KN 0.00 19.83 Vertical component of Earth pressure 18.10KN 0.00 2.87
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.26 -9.315 Water current force on deck slab 3.80KN 2.19 -1.36 Water current force on abutment 3.38KN 1.98 -1.17 Frictional force due to water on deck slab 4.96KN 2.19 -1.78 Frictional force due to water on abutment 0.50KN 0.60 -0.1
31.92
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 143.07KN 0.00 22.712 Net self wieght of abutment&footings 124.74KN 0.00 19.83 Vertical component of Earth pressure 18.10KN 0.00 2.87
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.26 9.315 Water current force on deck slab 3.80KN 2.19 1.36 Water current force on abutment 3.38KN 1.98 1.17 Frictional force due to water on deck slab 4.96KN 2.19 1.78 Frictional force due to water on abutment 0.50KN 0.60 0.1
58.84
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 31.92 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 58.84 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 (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)
1 Reaction due to dead load from super structure 338.55KN 0.00 0.00
2 Self wieght of abutments 155.52KN 0.075 0.000
3 Reaction due to live load with impact factor 399.88KN -0.01 0.543
4 Vertical component of Active Earth pressure 18.10KN 0.525 0.00
912.05KN
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 3.26
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction 2.96
3 Horizontal Active Earth pressure force 67.60KN y-Direction 0.53
133.44KN
Check for stability against over turning:-
Taking moments of all the overturning forces about toe of the abutment wrt x-axis,
Moment due to tractive,braking&frictional resistance of bearings = 141.61Kn-m
Moment due to active earth pressure force = 36.05Kn-m
Total overturning moment = 177.66Kn-m
Taking moments of all the restoring forces about toe of the abutment wrt x-axis,,
Moment due to dead load reaction from super structure = 177.74Kn-m
Moment due to self weight of abutment = 93.31Kn-m
Moment due to live load reaction on abutment = 205.94Kn-m
Moment due to vertical component of active earth pressure = 19.01Kn-m
Total Restoring moment = 496.00Kn-m
Factor of safety = 2.79181252 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)
Check for stability against sliding:-
912.05KN
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Location(Ht.from the section considered).(m)
Total vertical load acting on the base of the abutment Vb =
133.44KN
Coefficient of friction between concrete surfaces = 0.80
5.46799594 > 1.5 Hence safe
(As per clause 706.3.4 of IRC:78-2000)
b)Load Envelope-II:-(The Canal is full,back fill intact with no live load on span)
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 338.55KNDeduct uplift pressure -195.48KNNet reaction due to dead load from super structure 143.07KN 0.00 0.00
Self wieght of abutments 155.52KN
-64.80KN
2 Net self wieght 90.72KN 0.075 0.000
3 Vertical component of Active Earth pressure 18.10 0.525 0.00
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 3.26
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction 0.00
3 Active Earth pressure force 67.60KN y-Direction 0.53
4 Force due to water pressure 11.48KN y-Direction 0.71
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 = 36.05Kn-m
Total overturning moment = 36.05Kn-m
Taking moments of all the restoring forces about toe of the abutment wrt x-axis,
Total sliding force,ie,horizontal load on the abutment Hb =
Factor of safety against sliding Fs =
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)
Moment due to dead load reaction from super structure = 75.11
Moment due to self weight of abutment = 54.43Kn-m
Moment due to water pressure force on the abutment = 8.10Kn-m
Moment due to vertical component of active earth pressure = 19.01Kn-m
Total Restoring moment = 156.65Kn-m
Factor of safety = 4.34515347 > 2.0 Hence safe(As per clause 706.3.4 of IRC:78-2000)
Check for stability against sliding:-
251.89KN
67.60KN
Coefficient of friction between concrete surfaces = 0.80
2.98107738 > 1.5 Hence safe
(As per clause 706.3.4 of IRC:78-2000)
VI)Design of Strip footing:-
a)Load Envelope-III:-(The Canal is dry,back fill intact with live load on span)
i)At the bottom of RCC strip footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 338.55KN 0.00 0.00
2 Self weight of abutment&footings 349.92KN 0.015 0.000
3 138.21KN 0.00 0.00
4 Reaction due to live load with impact factor 295.77KN 0.00 0.543
4 Vertical component of earth pressure 18.10KN 0.525 0.000
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)
Self weight of RCC strip footing
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction 4.46
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction 4.16
3 Horizontal load due to earth pressure 67.60KN y-Direction 1.73
Safe bearing capacity SBC of the soil = 15.00t/sqm
Check for stresses:-
About x-axis:-
Breadth of footing b = 6.30m
Depth of footing d = 1.95m
Area of the footing = A = 12.285
Section modulus of bottom footing 3.99
about x-axis --Zx =
For RCC Strip footing permissible bearing pressure is 1.5xSBC = 225KN/sqm
No tension is allowed on soil as per clause 706.3.3.1 of IRC 78:2000
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 27.562 Self wieght of abutment&footings 349.92KN 0.02 28.893 Self weight of RCC strip footing 138.21KN 0.00 11.254 Reaction due to live load with impact factor 295.77KN 0.00 24.08
5 Vertical component of Earth pressure 18.10KN 0.53 2.21Horizontal loads:- (Stress = M/Z)
1 Wind load 18.00KN 0.00 02 Tractive,Braking&Frictional resistance of bearings 47.84KN 4.16 -49.93 Horizontal load due to earth pressure 67.60KN 1.73 -29.4
14.79
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 27.562 Self wieght of abutment&footings 349.92KN -0.02 28.083 Self weight of RCC strip footing 138.21KN 0.00 11.254 Reaction due to live load with impact factor 295.77KN 0.00 24.08
5 Vertical component of Earth pressure 18.10KN -0.53 0.74Horizontal loads:- (Stress = M/Z)
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
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)
1 Wind load 18.00KN 0.00 02 Tractive,Braking&Frictional resistance of bearings 47.84KN 4.16 49.853 Horizontal load due to earth pressure 67.60KN 1.73 29.35
170.91
Stress at heel = P/A(1+6e/b)+M/Z = 14.79 KN/Sqm>0
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 170.91 KN/Sqm<225KN/sqm
Hence safe.
About y-axis:-
Breadth of footing b = 1.95mDepth of footing d = 6.30mArea of the footing = A = 12.285
Section modulus of bottom footing 12.90
about y-axis --Zy =
For RCC Strip footing permissible bearing pressure is 1.5xSBC = 225KN/sqm
No tension is allowed on soil as per clause 706.3.3.1 of IRC 78:2000
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 27.562 Self wieght of abutment&footings 349.92KN 0.00 28.483 Self weight of RCC strip footing 138.21KN 0.00 11.254 Reaction due to live load with impact factor 295.77KN -0.543 -16.155 Vertical component of Earth pressure 18.10KN 0.00 1.47
Horizontal loads:- (Stress = M/Z)1 Wind load 18.00KN 4.46 -6.222 Tractive,Braking&Frictional resistance of bearings 47.84KN 0.00 0.03 Horizontal load due to earth pressure 67.60KN 0.00 0.0
46.39
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 338.55KN 0.00 27.562 Self wieght of abutment&footings 349.92KN 0.00 28.483 Self weight of RCC strip footing 138.21KN 0.00 11.254 Reaction due to live load with impact factor 295.77KN 0.543 64.35 Vertical component of Earth pressure 18.10KN 0.00 1.47
Horizontal loads:- (Stress = M/Z)1 Wind load 18.00KN 4.46 6.222 Tractive,Braking&Frictional resistance of bearings 47.84KN 0.00 03 Horizontal load due to earth pressure 67.60KN 0.00 0
139.28
m2
(1/6)bd2 = m3
Intensity in KN (P)
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)
Stress at up stream side edge of abutment = P/A(1+6e/b)+M/Z = 46.39 KN/Sqm>0
Hence safe.Stress at down stream side edge of abutment = P/A(1+6e/b)+M/Z = 139.29 KN/Sqm<225KN/sqm
Hence safe.
The footing has to be designed as strip footing supporting the masonry structure
The net bearing pressure on the toe of footing = 159.66 KN/Sqm(Excluding self weight of footing)
The footing needs to be designed for 1.5 times the above net bearing pressure 239.49 KN/Sqm
The UDL on the footing for unit width = 239.49 KN/m
The critical section for bending is at a distance of 1/4xwidth of bottom footing from the centre,ie,at section X--X
Hence,the length of cantilever portion to be considered for design =
0.83m
82.49KN-m
Effective depth required d = 157.51mm
The over all depth required(Assuming 16mm dia bars) = 215.51mm
However provide overall depth of = 450.00mm
Hence,effective depth = 392.00mm
Hence,the critical bending moment = (1/2)Wl2 =
Mu/0.133fckb =
b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4
X
Y
Y
d3d3
Bottom steel:-
0.537
From table 3 of SP 16,percentage of steel required = 0.156
Area of steel required = 611.52sqmm
Hence provide 12mm dia bars at 125mm c/c along width,the area of reinforcement comes to
904.32sqmmDistribution steel:-
Provide distribution reinforcement of 0.15% of cross sectional area of footing
Hence,the distribution reinforcement required = 675.00sqmm
Adopting 12mm dia bars,the spacing required = 167.00mm
However provide 12mm dia bars at 150mm c/c spacing,as distribution reinforcement
Check for one way shear:-
The critical section for beam shear is at distance of 'd' from the face of the column,ie,at Y-Y
35.92KN
0.1N/sqmm <2.8 N/sqmm(As per Table 20 of 1S 456)
Hence,the section is safe from shear point of view
Assumed percentage area of the steel reinforcement = 0.23%
The design shear strength of concrete for the above steel percentage from Table 19 of IS 456 is
0.35 137.20KN
0.35>0.1
Hence,the depth provided is safe from beam shear point of view
The check for two way shear is not necessary in the present context.
Mu/bd2 =
Hence,the factored design shear force VFd =
Nominal shear stress Tv =
Hence Vuc =
Design of pier for bridge
I)Design Parameters:-
Clear Right Span = 6.00m
= 6.800m
Width of the carriage way = 6.00m
Thickness of deck slab as per IRC SP 20 = 0.480m
= 0.075m
Height of guard stones = 0.750m
Thickness of pier bed block = 0.30m
Sectional area of pier bed block = 0.410sqm
Thickness of strip footing = 0.45m
Height of pier = 1.200m
(As per hydralic calculations)
Top width of pier = 0.900m
Bottom width of pier = 0.90m
Sectional area of pier section = 1.080sqm
One side batter of pier = 0.000m
Other side batter of pier = 0.000m
Width of 1st footing = 1.20m
Thickness of 1st footing = 0.30m
One side offset of 1st footing wrt pier = 0.15m
Other side offset of 1st footing wrt pier = 0.15m
= 1.50m
= 0.30m
One side offset of 2nd footing wrt pier = 0.30m
Other side offset of 2nd footing wrt pier = 0.30m
Width of 3rd footing = 1.80m
Thickness of 3rd footing = 0.30m
One side offset of 3rd footing wrt pier = 0.45m
Other side offset of 3rd footing wrt pier = 0.45m
Width of VRCC strip footing = 2.40m
Deck slab length
Thickness of wearing coat
Width of 2nd footing
Thickness of 2nd footing
= 0.45m
= 0.75m
= 0.75m
Offset of top footing along width = 0.00m
Offset of 2nd footing along width = 0.00m
Offset of 3rd footing along width = 0.00m
= 0.15m
Type of bearings = No bearings proposed
= 25KN/cum
= 24KN/cum
= 5.645m
= 3.965m
= 6.235m
= 2.315m
= 15.00t/sqm
= 20.00N/sqmm
= 25.00N/sqmm
= 415.00N/sqmm
Cover to reinforcement = 50.00mm
= 10KN/cum
II)General loading pattern:-
As per IRC:6---2000,the following loadings are to be considered on the bridge or slabculvert:-
1.Dead load2.Live load3.Impact load4.Wind load5.Water current6.Tractive,braking effort of vehicles&frictional resistance of bearings7.Buoyancy8.Seismic force9.Water pressure force
Apart from the above forces,the following pressures are to be considered as per clause 7.11.2.2 of IRC SP:82---2007:-
(a) Pressure due to static head due to afflux on upstream side and trough of
Thickness of VRCC strip footing (d3)
Canal side offset of RCC strip footing wrt pier (s5)
Bank side offset of RCC strip footing wrt pier (s6)
Offset of RCC strip footing along width (w1)
Unit weight of RCC (yrc)
Unit weight of PCC (ypc)
Road crest level (RTL)
Low bed level (LBL)
High flood Level (HFL)Bottom of foundation level (BFL) Safe Bearing Capacity of the soil (SBC)
Compressive strength of concrete for PCC (fck)
Compressive strength of concrete for VRCC Strip footing (fck)
Yield strength of steel (fy)
Unit weight of water (w)
standing wave on down stream side:
(b) Pressure due to velocity head
(c) Pressure due to eddies
(d) Pressure due to friction of water against piers and bottom of slab
(e) Force due to uplift under superstructure
super structure should also be considered:
As per clause 202.3,the increase in permissible stresses is not permissible for theabove loading combination.
III)Loading on the slab culvert for design of pier:-
1.Dead Load:-
i)Self wieght of the deck slab = 489.60KN
ii)Self wieght of bed block over pier = 61.50KN
iii)Self weight of wearing coat = 76.50KN
627.60KN
There is no need to consider snow load as per the climatic conditions
Self wieght of the pier upto bottom most footing based on the preliminary section assumed:-
iv)Self wieght of the pier section = 155.52KN
v)Self wieght of top footing = 51.84KN
vi)Self wieght of 2nd footing = 64.80KN
vii)Self wieght of 3rd footing = 77.76KN
As per the clause 7.11.3.4 of IRC:SP82--2007,Additional load of 150 mm thick silt with density equal to 15 kN/m 3 spread over the entire soffit(in case of box girders) and deck slabs of all types of
viii)Self wieght of 4th footing = 0.00KN
349.92KN
ix)Calculation of eccentricity of self weight of pier w.r.t base of pier
S.No Description Load in KN Distance of centroid of load from toe of pier
1 0 0.9
2 155.52 0.45
3 0 0
155.52
Location of resultant from toe of pier = 0.45m
Eccentricity wrt centre of base of pier = 0.000m
Back batter(W1)
Centre portion(W2)
Front batter(W3)
W1
W2
W3
b1
b2 b1 b3
x)Calculation of eccentricity of self weight of pier&1st footing w.r.t bottom of 1st footing
S.No Description Load in KN
1 Back batter 0 1.05
2 Centre portion 155.52 0.6
3 Front batter 0 0.15
4 1st footing 51.84 0.6
207.36
Location of resultant from toe of pier = 0.60m
Eccentricity wrt centre of 1st footing= 0.000m
xi)Calculation of eccentricity of self weight of pier,1st&2nd footings w.r.t bottom of 2nd footing
S.No Description Load in KN
1 Back batter 0 1.2
2 Centre portion 155.52 0.75
3 Front batter 0 0.3
4 1st footing 51.84 0.75
Distance of centroid of load from toe of 1st footing
Distance of centroid of load from toe of 2nd footing
5 2nd footing 64.8 0.75
272.16
Location of resultant from toe of pier = 0.75m
Eccentricity = 0.000m
xii)Calculation of eccentricity of self weight of pier,1st&2nd footings w.r.t bottom of 2nd footing
S.No Description Load in KN
1 Back batter 0 1.352 Centre portion 155.52 0.93 Front batter 0 0.454 1st footing 51.84 0.905 2nd footing 64.8 0.906 3rd footing 77.76 0.90
349.92
Location of resultant from toe of pier = 0.90m
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 3rd footing
are to be designed for IRC Class A loading.
2.7t
2.7t
11.4
t
11.4
t
6.8t
6.8t
6.8t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
clauses 207.1.3&207.4
The ground contact area of wheels for the above placement,each axle wise isgiven below:-
Axle load Ground Contact Area(Tonnes) B(mm) W(mm)
The IRC Class A loading as per the drawing is severe and the same is to be considered as per
2.7t
2.7t
11.4
t
11.4
t
6.8t
6.8t
6.8t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
Y
X
6800
1200
4300
11.4t
11.4t
6.8t
1800
450
2750 3250
Area to be loadedwith 5KN/m² liveload + 2.25KN/m²silt load
11.4 250 5006.8 200 3802.7 150 200
Assuming 0.3m allowance for guide posts and the clear distance of vehicle from
the edge of guide post being 0.15m as per clause 207.1,the value of 'f' shown in the figure will
be 0.45m
0.45m
3.25m
3.70m
The total live load on the deck slab composes the following components:-
1.Wheel loads----Point loads
2.Live load in remaing portion(Left side)----UDL
2.Live load in remaing portion(Right side)----UDL
Resultant live load:-
Eccentricity of live load w.r.t y-direction(Along the direction of travel of vehicles)
Taking moments of all the forces w.r.t y-axis
S.No Distance from Y-axis
1 57 0.70m
2 57 0.70m
3 57 2.50m
4 57 2.50m
Hence,the width of area to be loaded with 7.25KN/m2 on left side is (f) =
Similarly,the area to be loaded on right side (k) =
Wheel Load/UDL in KN
5 34 0.64m
6 34 2.44m
7 22.185 0.225m
8 160.225 4.375m
478.410
Distance of centroid of forces from y-axis
= 2.457m
Eccentricity = 0.543m
Eccentricity of live load w.r.t x-direction(At right angle to the travel of vehicles)
Taking moments of all the forces w.r.t x-axis
S.No Load in KN Distance from X-axis
1 34 0.925m
2 34 0.925m
5 57 5.225m
6 57 5.225m
7 57 6.425m
8 57 6.425m
9 22.19KN 3.400m
10 160.23KN 3.400m
478.41
Distance of centroid of forces from x-axis
= 4.204m
Eccentricity = 0.804m
Calculation of reactions on pier:-
421.85KN
56.56KN
Hence,the critical reaction is Ra = 421.8KN
The corrected reaction = 421.85KN
Reaction due to point loads Ra =
Reaction due to point loads = Rb =
Y
X
6800
2750 3250
804
543
Assuming that the live load reaction acts at the centre of the contact area on the pier,
The eccentricty of the line of action of live load = 0.00m
The eccentricity in the other direction need not be considered due to high section modulus in transverse direction.
3.Impact of vehicles:-
As per Clause 211 of IRC:6--2000,impact allowance shall be made by an increment
of live load by a factor 4.5/(6+L)
220220
460
900
1200
Hence,the factor is 0.352
Further as per clause 211.7 of IRC:6--2000,the above impact factor shall be only
50% for calculation of pressure on piers and abutments just below the level of bed block.There
is no need to increase the live load below 3m depth.
As such,the impact allowance for the top 3m of pier will be
For the remaining portion,impact need not be considered.
4.Wind load:-
The deck system is located at height of (RTL-LBL) 1.68m
The Wind pressure acting on deck system located at that height is considered for design.
As per clause 212.3 and from Table .4 of IRC:6---2000,the wind pressure at that hieght is=
59.48
Height of the deck system = 1.755
Breadth of the deck system = 7.4
The effective area exposed to wind force =HeightxBreadth =
Hence,the wind force acting at centroid of the deck system =(Taking 50% perforations)
Further as per clause 212.4 of IRC:6---2000 ,300 Kg/m wind force is considered to be
acting at a hieght of 1.5m from road surface on live load vehicle.
Hence,the wind force acting at 1.5m above the road surface =
The location of the wind force from the top of RCC strip footing =
5.Water current force:-
a)Water current force on deck slab:-
Kg/m2.
284.7
(where the value of 'K' is 1.5 )
Force acting on centroid of deck slab = 10.74KN
Point of action of water current force from the top of RCC strip footing =
b)Water current force on pier:-
Water pressure is considered on square ended piers as per clause 213.2 of
IRC:6---2000 is
Hence,the water current force = 4.30KN
Point of action of water current force from the top of RCC strip footing =
6.Tractive,braking effort of vehicles&frictional resistance of bearings:-
The breaking effect of vehicles shall be 20% of live load acting in longitudinal
direction at 1.2m above road surface as per the clause 214.2 of IRC:6--2000.
As no bearings are assumed in the present case,50% of the above longitudinal
force can be assumed to be transmitted to the supports of simply supported spans resting on
stiff foundation with no bearings as per clause 214.5.1.3 of IRC:6---2000
Hence,the longitudinal force due to braking,tractive or frictional resistance of
bearings transferred to pier is
47.84KN
The location of the tractive force from the top of RCC strip footing =
Velocity of stream at top,when the flow approaches the top of deck slab = √2 x Vmean =
P = 52KV2 = Kg/m2.
7.Buoyancy :-
As per clause 216.4 of IRC:6---2000,for abutments or piers of shallow depth,the dead weight of the pier shall be reduced by wieght of equal volume of water upto HFL.
The above reduction in self wieght will be considered assuming that the back fill behind the pier is scoured.
For the preliminary section assumed,the volume of pier section is
i)Volume of pier section = 6.48Cum
ii)Volume of top footing = 2.16Cum
iii)Volume of 2nd footing = 2.70Cum
iv)Volume of 3rd footing = 3.24Cum
v)Volume of 4th footing = 0.00Cum
14.58Cum
Reduction in self wieght = 145.80KN
9.Siesmic force :-
As per clause 222.1 of IRC:6---2000,the bridges in siesmic zones I and II need not be
designed for siesmic forces.The location of the slab culvert is in Zone-I.Hence,there is no need to
design the bridge for siesmic forces.
10.Water pressure force:-
As per clause 7.11.2.2(b) of IRC SP82:2007,the pressure due to static head will be zero at the surface of
water and will increase linearly to P = wh at depth 'h' from the surface, below which it will be constant as indicated
in the sketch below :-
Where, w = unit weight of water
h = afflux or depth of superstructure (including wearing coat) whichever is more.
555 5.55KN/m²
1125
Total horizontal water pressure force = 16.09KN
The above pressure acts at height of 0.42H = 0.71m
11.Pressure due to eddies :-
2gWhere,
V = velocity of approach(w = unit weight of water; g= Acceleration due to gravity)
Pressure force due to eddies = 0.014KN
which is negligible.Hence it need not be considered
12. Pressure due to friction of water against piers and bottom of slab :-
Where,
ρ = mass density of water (w/g)
C = value of constant generally taken as10%
Pressure due to eddies = w (Vv-V)2
Vv = velocity of flow through the vents,
Pressure due to friction =f x ρ x (Cx Vv)2
f = friction coefficient = 1
Vv = velocity of flow through the vents (m/sec)
555 5.55KN/m²
1125
i)Force due to friction on Deck slab:-
Frictional force on bottom and top of deck slab = 4.96KN
The location of the frictional force from the top of RCC strip footing =
ii)Force due to friction on pier:-
Frictional force on both faces of pier = 0.50KN
The location of the frictional force from the top of RCC strip footing =
13. Force due to uplift under superstructure :-
This force acts vertically upwards and is given by
Where,
h = the uplift head under the deckslab which may be taken as higher of the following two values: (i) Afllux(ii) Thickness of superstructure including wearing coat-head loss due to increase in
following expression
2g
Where,
V = velocity of approach
Afflux = 0.131m
Head loss due to increase in velocity = 0.012m
Hence,up lift head = 0.543m
Hence uplift force on the deck slab = 221.54KN
IV)Check for stresses for pier&footings:-
a)Load Envelope-I:-(The Canal is dry,with live load on span)
i)On top of RCC Strip footing
The following co-ordinates are assumed:-
Uplift force = wh x Asp
Asp area of the superstructure in plan
velocity through vents (Vv) Head loss due to increase in velocity through the vents is calculated by
h1 = Vv2-V2
Vv =velocity of flow through the vents
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 627.60KN 0.00
2 Self wieght of pier&footings 349.92KN 0.000
3 421.85KN 0.00
4 Impact load 0.00 0.00
1399.37
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction
3 Water current force 0.00KN x-Direction
Check for stresses:-
About x-axis:-
Breadth of bottom footing b = 6.00m
Depth of bottom footing d = 1.80m
Area of the footing = A = 10.8
Section modulus of bottom footing 3.24
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
Vertical forces acting on the pier (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Reaction due to live load with impact factor---(Wheel loads+UDL)
Horizontal forces acting/transferred on the pier (H) composes of the following components
Intensity in KN
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Reaction due to live load with impact factor 421.85KN 0.004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.86
(Stress = -31.36*4.93/6.38)
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Reaction due to live load with impact factor 421.85KN 0.004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.86
(Stress = 31.36*4.93/6.38)
Stress at heel = P/A(1+6e/b)+M/Z = 72.57 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 186.57 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of bottom footing b = 1.80m
Depth of bottom footing d = 6.00m
Area of the footing = A = 10.8
Section modulus of bottom footing about = 10.80
y-axis--Zy =
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression is 5N/mm2
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Reaction due to live load with impact factor 421.85KN -0.5434 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 4.166 Water current force 0.00KN 0.00
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Reaction due to live load with impact factor 421.85KN 0.5434 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 4.166 Water current force 0.00KN 0.00
Stress at up stream side P/A(1+6e/b)+M/Z = 101.43 KN/Sqm>-2800KN/sqm.edge of pier =
Hence safe.
Stress at down stream side P/A(1+6e/b)+M/Z = 157.71 KN/Sqm<5000KN/sqmedge of pier =
Hence safe.
ii)On top of 3rd footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
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
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 627.60KN 0.00
2 Self wieght of pier&footings 272.16KN 0.000
3 Reaction due to live load with impact factor 421.85KN 0.00
4 Impact load 0.00 0.00
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction
3 Water current force 0.00KN x-Direction
Check for stresses:-
About x-axis:-
Breadth of 1st footing b = 6.00mDepth of 1st footing d = 1.50mArea of the footing = A = 9
Section modulus of Ist footing about 2.25
x-axis--Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical load acting on the pier (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the pier (H) composes of the following components
Intensity in KN
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 272.16KN 0.003 Reaction due to live load with impact factor 421.85KN 0.004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.56
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 272.16KN 0.003 Reaction due to live load with impact factor 421.85KN 0.004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.56
Stress at heel = P/A(1+6e/b)+M/Z = 71.15 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 222.54 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 1.50mDepth of 1st footing d = 6.00mArea of the footing = A = 9
Section modulus of Ist footing about 9.00
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 compression is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 272.16KN 0.003 Reaction due to live load with impact factor 421.85KN -0.5434 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.866 Water current force 0.00KN -0.30
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 272.16KN 0.003 Reaction due to live load with impact factor 421.85KN 0.5434 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.866 Water current force 0.00KN -0.30
Stress at up stream side P/A(1+6e/b)+M/Z = 113.67 KN/Sqm>-2800KN/sqm.edge of pier =
Hence safe.
Stress at down stream side P/A(1+6e/b)+M/Z = 180.01 KN/Sqm<5000KN/sqmedge of pier =
Hence safe.
i)On top of 2nd footing
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
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
Eccentricity/Lever arm
Vertical load acting on the pier (P) composes of the following components
S.No Type of load
1 Reaction due to dead load from super structure 627.60KN 0.00
2 Self wieght of pier&footings 207.36KN 0.000
3 Reaction due to live load with impact factor 496.09KN 0.00
4 Impact load 0.00 0.00
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction
3 Water current force 0.00KN x-Direction
Check for stresses:-
About x-axis:-
Breadth of pier b = 6.00mDepth of pier d = 1.20mArea of the footing = A = 7.2
Section modulus of base of pier 1.44
about x-axis--Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 207.36KN 0.003 Reaction due to live load with impact factor 496.09KN 0.00
Intensity in KN
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
4 Impact load 0.00KN 0.00Horizontal loads:- (Stress = M/Z)
5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.26
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 207.36KN 0.003 Reaction due to live load with impact factor 496.09KN 0.004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 3.26
Stress at heel = P/A(1+6e/b)+M/Z = 76.56 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 293.18 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of pier b = 1.20mDepth of pier d = 6.00mArea of the footing = A = 7.2
Section modulus of base of pier 7.20
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 compression is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 207.36KN 0.003 Reaction due to live load with impact factor 496.09KN -0.5434 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.566 Water current force 0.00KN -0.60
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 207.36KN 0.003 Reaction due to live load with impact factor 496.09KN 0.5434 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.566 Water current force 0.00KN -0.60
Stress at up stream side edge of pier = P/A(1+6e/b)+M/Z = 138.56 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of pier = P/A(1+6e/b)+M/Z = 231.18 KN/Sqm<5000KN/sqm
Hence safe.
i)On top of 1st footing
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 (P)
Eccentricity/Lever arm
Intensity in KN (P)
Eccentricity/Lever arm
Vertical load acting on the pier (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&cut waters 155.52KN 0.0003 Reaction due to live load with impact factor 421.85KN 0.00
4 Impact load 0.00 0.00
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction3 Water current force 0.00KN x-Direction
Check for stresses:-
About x-axis:-
Breadth of pier b = 6.00mDepth of pier d = 0.90mArea of the footing = A = 5.4
Section modulus of base of pier 0.81
about x-axis--Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 155.52KN 0.003 Reaction due to live load with impact factor 421.85KN 0.004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 2.96
Horizontal load acting/transferred on the pier (H) composes of the following components
Intensity in KN
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 155.52KN 0.003 Reaction due to live load with impact factor 421.85KN 0.004 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Tractive,Braking&Frictional resistance of bearings 47.84KN 2.96
Stress at heel = P/A(1+6e/b)+M/Z = 48.31 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 397.97 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of pier b = 0.90mDepth of pier d = 6.00mArea of the footing = A = 5.4
Section modulus of base of pier 5.40
about y-axis--Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 155.52KN 0.003 Reaction due to live load with impact factor 421.85KN -0.543
Intensity in KN (P)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression 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
4 Impact load 0.00KN 0.00Horizontal loads:- (Stress = M/Z)
5 Wind load 18.00KN 3.566 Water current force 0.00KN 0.00
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 155.52KN 0.003 Reaction due to live load with impact factor 421.85KN 0.5434 Impact load 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)5 Wind load 18.00KN 3.566 Water current force 0.00KN 0.00
Stress at up stream side edge of pier = P/A(1+6e/b)+M/Z = 168.85 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of pier = P/A(1+6e/b)+M/Z = 277.43 KN/Sqm<5000KN/sqm
Hence safe.
b)Load Envelope-II:-(The Canal is full,with no live load on span)
i)On top of RCC Strip footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 627.60KNDeduct uplift pressure -221.54KNNet Reaction due to dead load from super structure 406.06KN 0.00
Intensity in KN (P)
Eccentricity/Lever arm
Vertical load acting on the pier (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Self wieght of pier&cut waters 349.92KN
Reduction in self weight due to buoyancy -145.80KN
2 Net self weight 204.12KN 0.000
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction
3 Water current force on deck slab 10.74KN x-Direction
4 Water current force on pier 4.30KN x-Direction
5 Frictional force due to water on deck slab 4.96KN x-Direction
6 Frictional force due to water on pier 0.50KN x-Direction
7 Water pressure force 16.09KN y-Direction
Check for stresses:-
About x-axis:-
Breadth of bottom footing b = 6.00mDepth of bottom footing d = 1.80mArea of the footing = A = 10.8
Section modulus of bottom footing 3.24
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 204.12KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal load acting/transferred on the pier (H) composes of the following components
Intensity in KN
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
Intensity in KN (P)
Eccentricity/Lever arm
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 0.00KN 0.005 Water pressure force 16.09KN 1.61
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 204.12KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 0.00KN 0.005 Water pressure force 16.09KN 1.61
Stress at heel = P/A(1+6e/b)+M/Z = 64.47 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 48.53 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of bottom footing b = 1.80mDepth of bottom footing d = 6.00mArea of the footing = A = 10.8
Section modulus of bottom footing 10.80
about y-axis --Zy =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Intensity in KN (P)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression 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
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 204.12KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 4.165 Water current force on deck slab 10.74KN 3.096 Water current force on pier 4.30KN 2.107 Frictional force due to water on deck slab 4.96KN 3.098 Frictional force due to water on pier 0.50KN 1.50
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 204.12KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 4.165 Water current force on deck slab 10.74KN 3.096 Water current force on pier 4.30KN 2.107 Frictional force due to water on deck slab 4.96KN 3.098 Frictional force due to water on pier 0.50KN 1.50
Stress at up stream side edge of pier = P/A(1+6e/b)+M/Z = 44.17 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of pier = P/A(1+6e/b)+M/Z = 68.83 KN/Sqm<5000KN/sqm
Hence safe.
ii)On top of 3rd 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
Intensity in KN (P)
Vertical load acting on the pier (P) composes of the following components
S.No Type of load
1 Reaction due to dead load from super structure 627.60KNDeduct uplift pressure -221.54KNNet Reaction due to dead load from super structure 406.06KN 0.00
Self wieght of pier&cut waters 272.16KN
Reduction in self weight due to buoyancy -113.40KN
2 Net self weight 158.76KN 0.000
3 Vertical component of earth pressure 0.00KN 0.000
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction
3 Water current force on deck slab 10.74KN x-Direction
4 Water current force on pier 4.30KN x-Direction
5 Frictional force due to water on deck slab 4.96KN x-Direction
6 Frictional force due to water on pier 0.50KN x-Direction
7 Horizontal load due to earth pressure 0.00KN y-Direction
8 Water pressure force 16.09KN y-Direction
Check for stresses:-
About x-axis:-
Breadth of 1st footing b = 6.00mDepth of 1st footing d = 1.50mArea of the footing = A = 9
Section modulus of bottom footing 2.25
about x-axis --Zx =
i.e, 5000KN/sqm
Intensity in KN
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the pier (H) composes of the following components
Intensity in KN
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression is 5N/mm2
For M20 grade of concrete permissible tensile stress in bending tension is -2.8N/mm2
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 158.76KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 0.00KN 0.005 Water pressure force 16.09KN 1.31
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 158.76KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 0.00KN 0.005 Water pressure force 16.09KN 1.31
Stress at heel = P/A(1+6e/b)+M/Z = 72.1 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 53.42 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of 1st footing b = 1.50mDepth of 1st footing d = 6.00mArea of the footing = A = 9
Section modulus of bottom footing 9.00
about y-axis --Zy =
i.e, 5000KN/sqm
Intensity in KN (P)
Eccentricity/Lever arm
Intensity in KN (P)
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression is 5N/mm2
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 158.76KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.865 Water current force on deck slab 10.74KN 2.796 Water current force on pier 4.30KN 1.807 Frictional force due to water on deck slab 4.96KN 2.798 Frictional force due to water on pier 0.50KN 1.20
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 158.76KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.865 Water current force on deck slab 10.74KN 2.796 Water current force on pier 4.30KN 1.807 Frictional force due to water on deck slab 4.96KN 2.798 Frictional force due to water on pier 0.50KN 1.20
Stress at up stream side edge of pier = P/A(1+6e/b)+M/Z = 49.24 KN/Sqm>-2800KN/sqm.
Hence safe.Stress at down stream side edge of pier = P/A(1+6e/b)+M/Z = 76.28 KN/Sqm<5000KN/sqm
Hence safe.
iii)On top of 2nd footing
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)
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 627.60KNDeduct uplift pressure -221.54KNNet Reaction due to dead load from super structure 406.06KN 0.00
Self wieght of pier&footings 207.36KN
Reduction in self weight due to buoyancy -86.40KN
2 Net self weight 120.96KN 0.000
3 Vertical component of earth pressure 0.00KN 0.000
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction
3 Water current force on deck slab 10.74KN x-Direction
4 Water current force on pier 4.30KN x-Direction
5 Frictional force due to water on deck slab 4.96KN x-Direction
6 Frictional force due to water on pier 0.50KN x-Direction
7 Horizontal load due to earth pressure 0.00KN y-Direction
8 Water pressure force 16.09KN y-Direction
Check for stresses:-
About x-axis:-
Breadth of abutment b = 6.00mDepth of abutment d = 1.20mArea of the footing = A = 7.2
Vertical load acting on the pier (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the pier (H) composes of the following components
Intensity in KN
m2
Section modulus of bottom footing 1.44
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 120.96KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 0.00KN 0.005 Water pressure force 16.09KN 1.01
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 120.96KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 0.00KN 0.005 Water pressure force 16.09KN 1.01
Stress at heel = P/A(1+6e/b)+M/Z = 84.44 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 61.96 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of pier b = 1.20m
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression 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)
Depth of pier d = 6.00mArea of the footing = A = 7.2
Section modulus of bottom footing 7.20
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 406.06KN 0.002 Net self wieght of pier&footings 120.96KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.565 Water current force on deck slab 10.74KN 2.496 Water current force on pier 4.30KN 1.507 Frictional force due to water on deck slab 4.96KN 2.498 Frictional force due to water on pier 0.50KN 0.90
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 120.96KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.565 Water current force on deck slab 10.74KN 2.496 Water current force on pier 4.30KN 1.507 Frictional force due to water on deck slab 4.96KN 2.498 Frictional force due to water on pier 0.50KN 0.90
Stress at up stream side edge of pier = P/A(1+6e/b)+M/Z = 57.91 KN/Sqm>-2800KN/sqm.
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression 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 pier = P/A(1+6e/b)+M/Z = 88.49 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 vehiclesb)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 627.60KNDeduct uplift pressure -221.54KNNet Reaction due to dead load from super structure 406.06KN 0.00Self wieght of pier&footings 155.52KNReduction in self weight due to buoyancy -64.80KN
2 Net self weight 90.72KN 0.0003 Vertical component of earth pressure 0.00KN 0.000
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction3 Water current force on deck slab 10.74KN x-Direction4 Water current force on pier 4.30KN x-Direction5 Frictional force due to water on deck slab 4.96KN x-Direction6 Frictional force due to water on pier 0.50KN x-Direction7 Horizontal load due to earth pressure 0.00KN y-Direction8 Water pressure force 16.09KN y-Direction
Check for stresses:-
About x-axis:-
Breadth of pier b = 6.00mDepth of pier d = 0.90mArea of the footing = A = 5.4
Vertical load acting on the pier (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the pier (H) composes of the following components
Intensity in KN
m2
Section modulus of bottom footing 0.81
about x-axis --Zx =
i.e, 5000KN/sqm
i.e, -2800KN/sqm
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 90.72KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 0.00KN 0.005 Water pressure force 16.09KN 0.71
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 90.72KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 0.00KN 0.005 Water pressure force 16.09KN 0.71
Stress at heel = P/A(1+6e/b)+M/Z = 106.02 KN/Sqm>-2800KN/sqm.
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 77.98 KN/Sqm<5000KN/sqm
Hence safe.
About y-axis:-
Breadth of pier b = 0.90m
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression 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)
Depth of pier d = 6.00mArea of the footing = A = 5.4
Section modulus of bottom footing 5.40
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 406.06KN 0.002 Net self wieght of pier&footings 90.72KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Wind load 18.00KN 3.265 Water current force on deck slab 10.74KN 2.196 Water current force on pier 4.30KN 1.207 Frictional force due to water on deck slab 4.96KN 2.198 Frictional force due to water on pier 0.50KN 0.60
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 406.06KN 0.002 Net self wieght of pier&footings 90.72KN 0.003 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)4 Horizontal load due to earth pressure 18.00KN 3.265 Water current force on deck slab 10.74KN 2.196 Water current force on pier 4.30KN 1.207 Frictional force due to water on deck slab 4.96KN 2.198 Frictional force due to water on pier 0.50KN 0.60
Stress at up stream side edge of pier = P/A(1+6e/b)+M/Z = 73.74 KN/Sqm>-2800KN/sqm.
m2
(1/6)bd2 = m3
For M20 grade of concrete permissible compressive stress in direct compression 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 pier = P/A(1+6e/b)+M/Z = 110.26 KN/Sqm<5000KN/sqm
Hence safe.
V)Check for stability of pier:-
a)Load Envelope-I:-(The Canal is dry,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 627.60KN 0.00
2 Self wieght of pier 155.52KN 0.000
3 Reaction due to live load with impact factor 421.85KN 0.00
4 Vertical component of Active Earth pressure 0.00KN 0.000
1204.97KN
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction
3 Horizontal Active Earth pressure force 0.00KN y-Direction
65.84KN
Check for stability against over turning:-
Taking moments of all the overturning forces about toe of the pier wrt x-axis,
Moment due to tractive,braking&frictional resistance of bearings =
Vertical load acting on the pier (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Horizontal load acting/transferred on the abutment (H) composes of the following components
Intensity in KN
Moment due to active earth pressure force =
Total overturning moment =
Taking moments of all the restoring forces about toe of the pier wrt x-axis,,
Moment due to dead load reaction from super structure =
Moment due to self weight of pier =
Moment due to live load reaction on pier =
Moment due to vertical component of active earth pressure =
Total Restoring moment =
Factor of safety = 3.82908498 > 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 =
14.6409083 > 1.5 Hence safe
(As per clause 706.3.4 of IRC:78-2000)
b)Load Envelope-II:-(The Canal is full,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
Total vertical load acting on the base of the pier Vb =
Total sliding force,ie,horizontal load on the pier Hb =
Factor of safety against sliding Fs =
Vertical load acting on the pier (P) composes of the following components
S.No Type of load
1 Reaction due to dead load from super structure 627.60KNDeduct uplift pressure -221.54KNNet Reaction due to dead load from super structure 406.06KN 0.00
Self wieght of pier 155.52KN
-64.80KN
2 Net self wieght 90.72KN 0.000
3 Vertical component of Active Earth pressure 0.00 0.000
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 0.00KN y-Direction
3 Water current force on deck slab 10.74KN x-Direction
4 Water current force on pier 4.30KN x-Direction
5 Frictional force due to water on deck slab 4.96KN x-Direction
6 Frictional force due to water on pier 0.50KN x-Direction
7 Active Earth pressure force 0.00KN y-Direction
8 Force due to water pressure 16.09KN 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 =
Taking moments of all the restoring forces about toe of the abutment wrt x-axis,
Moment due to self weight of pier =
Intensity in KN
Eccentricty about x-axis(m)
Reduction in self weight due to buoyancy
Horizontal load acting/transferred on the pier (H) composes of the following components
Intensity in KN
Moment due to water pressure force on the pier =
Moment due to vertical component of active earth pressure =
Total Restoring moment =
Factor of safety = ∞ > 2.0 Hence safe
(As per clause 706.3.4 of IRC:78-2000)
Check for stability against sliding:-
Coefficient of friction between concrete surfaces =
∞ > 1.5 Hence safe
(As per clause 706.3.4 of IRC:78-2000)
VI)Design of Strip footing:-
a)Load Envelope-I:-(The Canal is dry,with live load on span)
i)At the bottom of RCC strip footing
The following co-ordinates are assumed:-
a)x-Direction-----At right angle to the movement of vehicles
b)y-Direction-----In the direction of movement of vehicles
S.No Type of load
1 Reaction due to dead load from super structure 627.60KN 0.00
2 Self weight of pier&footings 349.92KN 0.000
3 170.10KN 0.00
Total vertical load acting on the base of the pier Vb =
Total sliding force,ie,horizontal load on the pier Hb =
Factor of safety against sliding Fs =
Vertical load acting on the pier (P) composes of the following components
Intensity in KN
Eccentricty about x-axis(m)
Self weight of RCC strip footing
4 Reaction due to live load with impact factor 421.85KN 0.00
4 Vertical component of earth pressure 0.00KN 0.000
S.No Type of load Direction x or y
1 Wind load 18.00KN x-Direction
2 Tractive,Braking&Frictional resistance of bearings 47.84KN y-Direction
3 Horizontal load due to earth pressure 0.00KN y-Direction
Safe bearing capacity SBC of the soil = 15.00t/sqm
Check for stresses:-
About x-axis:-
Breadth of footing b = 6.30m
Depth of footing d = 2.40m
Area of the footing = A = 15.12
Section modulus of bottom footing 6.05
about x-axis --Zx =
For RCC Strip footing permissible bearing pressure is 1.5xSBC = 225KN/sqm
No tension is allowed on soil as per clause 706.3.3.1 of IRC 78:2000
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Self weight of RCC strip footing 170.10KN 0.004 Reaction due to live load with impact factor 421.85KN 0.00
5 Vertical component of Earth pressure 0.00KN 0.00Horizontal loads:- (Stress = M/Z)
1 Wind load 18.00KN 0.002 Tractive,Braking&Frictional resistance of bearings 47.84KN 4.163 Horizontal load due to earth pressure 0.00KN 0.00
Horizontal load acting/transferred on the pier (H) composes of the following components
Intensity in KN
m2
(1/6)bd2 = m3
Intensity in KN (P)
Eccentricity/Lever arm
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Self weight of RCC strip footing 170.10KN 0.004 Reaction due to live load with impact factor 421.85KN 0.00
5 Vertical component of Earth pressure 0.00KN 0.00Horizontal loads:- (Stress = M/Z)
1 Wind load 18.00KN 0.002 Tractive,Braking&Frictional resistance of bearings 47.84KN 4.163 Horizontal load due to earth pressure 0.00KN 0.00
Stress at heel = P/A(1+6e/b)+M/Z = 70.89 KN/Sqm>0
Hence safe.
Stress at toe = P/A(1+6e/b)+M/Z = 136.71 KN/Sqm<225KN/sqm
Hence safe.
About y-axis:-
Breadth of footing b = 2.40mDepth of footing d = 6.30mArea of the footing = A = 15.12
Section modulus of bottom footing 15.88
about y-axis --Zy =
For RCC Strip footing permissible bearing pressure is 1.5xSBC = 225KN/sqm
No tension is allowed on soil as per clause 706.3.3.1 of IRC 78:2000
S.No Type of load
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Self weight of RCC strip footing 170.10KN 0.00
Intensity in KN (P)
m2
(1/6)bd2 = m3
Intensity in KN (P)
Eccentricity/Lever arm
4 Reaction due to live load with impact factor 421.85KN -0.5435 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)1 Wind load 18.00KN 4.462 Tractive,Braking&Frictional resistance of bearings 47.84KN 0.003 Horizontal load due to earth pressure 0.00KN 0.00
S.No Type of load Eccentricity
Vertical loads:-(Stress = P/A(1+6e/b)1 Reaction due to dead load from super structure 627.60KN 0.002 Self wieght of pier&footings 349.92KN 0.003 Self weight of RCC strip footing 170.10KN 0.004 Reaction due to live load with impact factor 421.85KN 0.5435 Vertical component of Earth pressure 0.00KN 0.00
Horizontal loads:- (Stress = M/Z)1 Wind load 18.00KN 4.462 Tractive,Braking&Frictional resistance of bearings 47.84KN 0.003 Horizontal load due to earth pressure 0.00KN 0.00
Stress at up stream side edge of pier = P/A(1+6e/b)+M/Z = 60.87 KN/Sqm>0
Hence safe.Stress at down stream side edge of pier = P/A(1+6e/b)+M/Z = 146.73 KN/Sqm<225KN/sqm
Hence safe.
The footing has to be designed as strip footing supporting the masonry structure
The net bearing pressure on the toe of footing = 125.46 KN/Sqm(Excluding self weight of footing)
The footing needs to be designed for 1.5 times the above net bearing pressure 188.19 KN/Sqm
Intensity in KN (P)
b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4
X
Y
Y
d3d3
The UDL on the footing for unit width = 188.19 KN/m
The critical section for bending is at a distance of 1/4xwidth of bottom footing from the centre,ie,at section X--X
Hence,the length of cantilever portion to be considered for design =
0.83m
64.82KN-m
Effective depth required d = 139.62mm
The over all depth required(Assuming 16mm dia bars) = 197.62mm
However provide overall depth of = 450.00mm
Hence,effective depth = 392.00mm
Bottom steel:-
0.422
From table 3 of SP 16,percentage of steel required = 0.127Minimum percentage required = 0.15
Area of steel required = 588.00sqmm
However provide 12mm dia bars at 125mm c/c along width,the area of reinforcement comes to
904.32sqmmDistribution steel:-
Hence,the critical bending moment = (1/2)Wl2 =
Mu/0.133fckb =
Mu/bd2 =
b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4
X
Y
Y
d3d3
Provide distribution reinforcement of 0.15% of cross sectional area of footing
Hence,the distribution reinforcement required = 675.00sqmm
Adopting 12mm dia bars,the spacing required = 167.00mm
However provide 12mm dia bars at 150mm c/c spacing,as distribution reinforcement
Check for one way shear:-
The critical section for beam shear is at distance of 'd' from the face of the column,ie,at Y-Y
56.46KN
0.1N/sqmm <2.8 N/sqmm(As per Table 20 of 1S 456)
Hence,the section is safe from shear point of view
Assumed percentage area of the steel reinforcement = 0.23%
The design shear strength of concrete for the above steel percentage from Table 19 of IS 456 is
0.35 137.20KN
0.35>0.1
Hence,the depth provided is safe from beam shear point of view
The check for two way shear is not necessary in the present context.
Hence,the factored design shear force VFd =
Nominal shear stress Tv =
Hence Vuc =
Design of pier for bridge
No bearings proposed
thick silt with density
Moment
0
69.98
0
69.98
W1
W2
W3
b1
b2 b1 b3
Moment
0
93.31
0
31.1
124.41
Moment
0
116.64
0
38.88
48.6
204.12
Moment
0139.97
046.6658.3269.98
314.93
2.7t
2.7t
11.4
t
11.4
t
6.8t
6.8t
6.8t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
is severe and the same is to be considered as per
2.7t
2.7t
11.4
t
11.4
t
6.8t
6.8t
6.8t
6.8t
1.10
1.80
3.20 1.20 4.30 3.00 3.00 3.00
Y
X
6800
1200
4300
11.4t
11.4t
6.8t
1800
450
2750 3250
Area to be loadedwith 5KN/m² liveload + 2.25KN/m²silt load
296.00KN
22.19KN
160.23KN
478.41KN
Moment
39.90KNm
39.90KNm
142.50KNm
142.50KNm
21.76KNm
82.96KNm
4.99KNm
700.98KNm
1175.50KNm
Moment
31.45KNm
31.45KNm
297.83KNm
297.83KNm
366.22KNm
366.22KNm
75.43KNm
544.77KNm
2011.19KN
Y
X
6800
2750 3250
804
543
The eccentricity in the other direction need not be considered due to high section modulus in transverse
220220
460
900
1200
0.176
3.86KN
18.00KN
4.16m
3.65m/sec
3.09m
2.10m
3.86m
As per clause 7.11.2.2(b) of IRC SP82:2007,the pressure due to static head will be zero at the surface of
water and will increase linearly to P = wh at depth 'h' from the surface, below which it will be constant as indicated
555 5.55KN/m²
1125
555 5.55KN/m²
1125
3.09m
1.50m
h = the uplift head under the deckslab which may be taken as higher of the following two values: (i) Afllux
) Head loss due to increase in velocity through the vents is calculated by
0.00
0.000
0.543
0.00
4.16
3.86
0.00
Eccentricty about y-axis(m)
Location(Ht.from the section considered).(m)
58.1132.4
39.060
-57
72.57
58.1132.4
39.060
57
186.57
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at heelP/A(1+6e/b)
Stress at toeP/A(1+6e/b)
58.1132.4
17.850
-6.930
101.43
58.1132.4
60.270
6.930
157.71
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at upstream edgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
0.00
0.000
0.543
0.00
3.86
3.56
-0.30
Eccentricty about y-axis(m)
Location(Ht.from the section considered).(m)
Stress at heelP/A(1+6e/b)
69.7330.2446.87
0
-75.7
71.14
69.7330.2446.87
0
75.7
222.54
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at toeP/A(1+6e/b)
69.7330.2421.42
0
-7.720
113.67
69.7330.2472.32
0
7.720
180.01
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at upstream edgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
0.00
0.000
0.543
0.00
3.56
3.26
-0.60
87.1728.868.9
Eccentricty about y-axis(m)
composes of the following components
Location(Ht.from the section considered).(m)
Stress at heelP/A(1+6e/b)
0
-108.31
76.56
87.1728.868.9
0
108.31
293.18
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at toeP/A(1+6e/b)
87.1728.8
31.490
-8.90
138.56
87.1728.8
106.310
8.90
231.18
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at upstream edgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
Eccentricty about y-axis(m)
0.000.0000.543
0.00
3.562.960.00
116.2228.8
78.120
-174.83
48.31
Location(Ht.from the section considered).(m)
Stress at heelP/A(1+6e/b)
116.2228.8
78.120
174.83
397.97
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
116.2228.835.7
Stress at toeP/A(1+6e/b)
Stress at upstream edgeP/A(1+6e/b)
0
-11.870
168.85
116.2228.8
120.540
11.870
277.43
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
0.00
Stress at D/S edgeP/A(1+6e/b)
Eccentricty about y-axis(m)
0.000
4.16
0.00
3.09
2.10
3.09
1.50
1.61
37.618.9
0
Location(Ht.from the section considered).(m)
Stress at heelP/A(1+6e/b)
08.0
64.47
37.618.9
0
0-8.0
48.53
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at toeP/A(1+6e/b)
Stress at U/S EdgeP/A(1+6e/b)
37.618.9
0
-6.93-3.1-0.8-1.4-0.1
44.17
37.618.9
0
6.933.10.81.40.1
68.83
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at D/S edgeP/A(1+6e/b)
0.00
0.000
0.000
3.86
0.00
2.79
1.80
2.79
1.20
0.00
1.31
Eccentricty about y-axis(m)
Location(Ht.from the section considered).(m)
45.1217.64
0
09.3
72.1
45.1217.64
0
0-9.3
53.42
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at heelP/A(1+6e/b)
Stress at toeP/A(1+6e/b)
45.1217.64
0
-7.72-3.3-0.9-1.5-0.1
49.24
45.1217.64
0
7.723.30.91.50.1
76.28
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at U/S EdgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
0.00
0.000
0.000
3.56
0.00
2.49
1.50
2.49
0.90
0.00
1.01
Eccentricty about y-axis(m)
Location(Ht.from the section considered).(m)
56.416.8
0
011.2
84.44
56.416.8
0
0-11.261.96
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at heelP/A(1+6e/b)
Stress at toeP/A(1+6e/b)
56.416.8
0
-8.9-3.7-0.9-1.7-0.1
57.91
56.416.8
0
8.93.70.91.70.1
88.49
KN/Sqm>-2800KN/sqm.
Stress at U/S EdgeP/A(1+6e/b)
Stress at D/S edgeP/A(1+6e/b)
KN/Sqm<5000KN/sqm
0.00
0.0000.000
3.260.002.191.202.190.600.000.71
Eccentricty about y-axis(m)
Location(Ht.from the section considered).(m)
75.216.8
0
014.0
106.02
75.216.8
0
0-14.077.98
KN/Sqm>-2800KN/sqm.
KN/Sqm<5000KN/sqm
Stress at heelP/A(1+6e/b)
Stress at toeP/A(1+6e/b)
75.216.8
0
-10.87-4.4-1.0-2.0-0.1
73.74
75.216.8
0
10.874.41.02.00.1
110.26
KN/Sqm>-2800KN/sqm.
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
0.543
0.00
3.26
2.96
0.00
141.61Kn-m
Eccentricty about y-axis(m)
composes of the following components
Location(Ht.from the section considered).(m)
0.00Kn-m
141.61Kn-m
282.42Kn-m
69.98Kn-m
189.83Kn-m
0.00Kn-m
542.23Kn-m
(As per clause 706.3.4 of IRC:78-2000)
1204.97KN
65.84KN
0.80
(As per clause 706.3.4 of IRC:78-2000)
0.00
0.000
0.00
3.26
0.00
2.19
1.20
2.19
0.60
0.00
0.71
0.00Kn-m
0.00Kn-m
0.00Kn-m
40.82Kn-m
Eccentricty about y-axis(m)
Location(Ht.from the section considered).(m)
11.35Kn-m
0.00Kn-m
52.18Kn-m
(As per clause 706.3.4 of IRC:78-2000)
106.81KN
0.00KN
0.80
(As per clause 706.3.4 of IRC:78-2000)
0.00
0.000
0.00
Eccentricty about y-axis(m)
0.543
0.000
4.46
4.16
0.00
41.5123.1411.2527.9
0
0-32.90.0
Location(Ht.from the section considered).(m)
Stress at heelP/A(1+6e/b)
70.89
41.5123.1411.2527.9
0
032.91
0136.71
KN/Sqm<225KN/sqm
41.5123.1411.25
Stress at toeP/A(1+6e/b)
Stress at U/S edgeP/A(1+6e/b)
-9.970
-5.060.00.0
60.87
41.5123.1411.2565.77
0
5.0600
146.73
KN/Sqm<225KN/sqm
Stress at D/S edgeP/A(1+6e/b)
b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4
X
Y
Y
d3d3
The critical section for bending is at a distance of 1/4xwidth of bottom footing from the centre,ie,at section X--X
However provide 12mm dia bars at 125mm c/c along width,the area of reinforcement comes to
b2 b1 b3s1+b2+b1+b3+s2s3+b2+b1+b3+s4
X
Y
Y
d3d3
The critical section for beam shear is at distance of 'd' from the face of the column,ie,at Y-Y
Hence,the depth provided is safe from beam shear point of view
DESIGN OF FACE WALL (BIT-I)
Data:-
Height of Retaining wall =Height of wall above G.L=Height of wall below G.L=Density of back fill soil&material in toe portion = Unit weight of concrete =Top width =Bottom width assumed =Ground water Table level =
(in clock wise direction)
Surcharge over the back fill in terms of height of back fill =Safe bearing capacity =
Coefficient of active earth pressure by Coulomb's theory
Sin(a+Q)
sina sin(a-q) sin(Q+q)sin(Q-b)
sin(a+b)
From the above expression,
0.57
Hence,maximum pressure at the base of the wall Pa =
The pressure distribution along the height of the wall is as given below:-
Surcharge load = 615.6
615.6
2.40m
2462.40
Total earth pressure = 4432.32
The active earth pressure acts on the wall as shown below:-
0.30
Angle of shearing resistance of back fill material&material at toe portion(Q) = Angle of face of wall supporting earth with horizontal(a)(In degrees)
Slope of back fill(b) =Angle of wall friction (q) =
Ka =
Ka =
46.53
2.40m
63.470.3 C
0.151.50
Stability calculations:-Load(Kg)
Weight of the wall = 1728.00Kg3456.00Kg
Weight of the earth = 2592.00KgVertical component of Active earth pressure= 3215.43KgWeight of soil on the heel of footing-I = 1296.00Kg
12287.43Kg
Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.
Horizontal earth pressure force = 3050.65
Lever arm x = M = 0.65mV
Eccentricuty e = b/2-x = 0.10m <b/6
Maximum stress = P/A(1+6e/b) = 11468.27 < SBC Hence O.K
Minimum stress = P/A(1-6e/b) = 4914.97 Hence O.K
Coefficient of friction between soil and footing u = 0.5
1.81 >1.25
Factor of safety against overturning = 3.27 >1.5
Horizontal component of the earth pressure Ph =
Vertical component of the earth pressure Pv =
Factor of safety against sliding =(uFx0.9W)/Ph =
DESIGN OF FACE WALL (BIT-II)
Data:-
Height of Retaining wall =Height of wall above G.L=Height of wall below G.L=Density of back fill soil&material in toe portion = Grade of concrete =Grade of steel =Unit weight of concrete =Top width =Bottom width assumed =Ground water Table level =
(in clock wise direction)
Permissible compressive stress in bending for M20 Concrete (c)=Permissible tensile stress in bending for Fe 415 steel (t)=Modular ratio m = 280/3c =k = mc/(mc+t)j = 1-k/3 =R = 1/2(cjk) =Surcharge over the back fill in terms of height of back fill =Safe bearing capacity =
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,
0.57
Hence,maximum pressure at the base of the wall Pa =
The pressure distribution along the height of the wall is as given below:-
Surcharge load = 615.6
615.6
1.80m
Angle of shearing resistance of back fill material&material at toe portion(Q) = Angle of face of wall supporting earth with horizontal(a)(In degrees)
Slope of back fill(b) =Angle of wall friction (q) =
Ka =
Ka =
1846.80
Total earth pressure = 2770.2
The active earth pressure acts on the wall as shown below:-
0.30
46.53
1.80m
63.470.3 C
0.151.20
Stability calculations:-Load(Kg)
Weight of the wall = 1296.00Kg1944.00Kg
Weight of the earth = 1458.00KgVertical component of Active earth pressure= 2009.65KgWeight of soil on the heel of footing-I = 972.00Kg
7679.65Kg
Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.
Horizontal earth pressure force = 1906.65
Lever arm x = M = 0.53mV
Eccentricuty e = b/2-x = 0.07m <b/6
Maximum stress = P/A(1+6e/b) = 8639.6 < SBC Hence O.K
Minimum stress = P/A(1-6e/b) = 4159.81 Hence O.K
Coefficient of friction between soil and footing u = 0.5
Horizontal component of the earth pressure Ph =
Vertical component of the earth pressure Pv =
1.81 >1.25
Factor of safety against overturning = 3.36 >1.5
DESIGN OF FACE WALL (BIT-III)
Data:-
Height of Retaining wall =Height of wall above G.L=Height of wall below G.L=Density of back fill soil&material in toe portion = Grade of concrete =Grade of steel =Unit weight of concrete =Top width =Bottom width assumed =Ground water Table level =
(in clock wise direction)
Permissible compressive stress in bending for M20 Concrete (c)=Permissible tensile stress in bending for Fe 415 steel (t)=Modular ratio m = 280/3c =k = mc/(mc+t)j = 1-k/3 =R = 1/2(cjk) =Surcharge over the back fill in terms of height of back fill =Safe bearing capacity =
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,
0.51
Hence,maximum pressure at the base of the wall Pa =
The pressure distribution along the height of the wall is as given below:-
Surcharge load = 550.8
Factor of safety against sliding =(uFx0.9W)/Ph =
Angle of shearing resistance of back fill material&material at toe portion(Q) = Angle of face of wall supporting earth with horizontal(a)(In degrees)
Slope of back fill(b) =Angle of wall friction (q) =
Ka =
Ka =
550.8
1.20m
1101.60
Total earth pressure = 1321.92
The active earth pressure acts on the wall as shown below:-
0.30
42.59
1.20m
67.410.3 C
0.150.80
Stability calculations:-Load(Kg)
Weight of the wall = 864.00Kg720.00Kg
Weight of the earth = 540.00KgVertical component of Active earth pressure= 894.24KgWeight of soil on the heel of footing-I = 648.00Kg
3666.24Kg
Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.
Horizontal earth pressure force = 973.55
Lever arm x = M = 0.36mV
Horizontal component of the earth pressure Ph =
Vertical component of the earth pressure Pv =
Eccentricuty e = b/2-x = 0.04m <b/6
Maximum stress = P/A(1+6e/b) = 5957.64 < SBC Hence O.K
Minimum stress = P/A(1-6e/b) = 3207.96 Hence O.K
Coefficient of friction between soil and footing u = 0.5
1.69 >1.25
Factor of safety against overturning = 3.05 >1.5
DESIGN OF FACE WALL (BIT-IV)
Data:-
Height of Retaining wall =Height of wall above G.L=Height of wall below G.L=Density of back fill soil&material in toe portion = Grade of concrete =Grade of steel =Unit weight of concrete =Top width =Bottom width assumed =Ground water Table level =
(in clock wise direction)
Permissible compressive stress in bending for M20 Concrete (c)=Permissible tensile stress in bending for Fe 415 steel (t)=Modular ratio m = 280/3c =k = mc/(mc+t)j = 1-k/3 =R = 1/2(cjk) =Surcharge over the back fill in terms of height of back fill =Safe bearing capacity =
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,
0.42
Hence,maximum pressure at the base of the wall Pa =
Factor of safety against sliding =(uFx0.9W)/Ph =
Angle of shearing resistance of back fill material&material at toe portion(Q) = Angle of face of wall supporting earth with horizontal(a)(In degrees)
Slope of back fill(b) =Angle of wall friction (q) =
Ka =
Ka =
The pressure distribution along the height of the wall is as given below:-
Surcharge load = 453.6
453.6
0.80m
604.80
Total earth pressure = 604.8
The active earth pressure acts on the wall as shown below:-
0.30
34
0.80m
760.3 C
0.150.50
Stability calculations:-Load(Kg)
Weight of the wall = 576.00Kg192.00Kg
Weight of the earth = 144.00KgVertical component of Active earth pressure= 338.05KgWeight of soil on the heel of footing-I = 432.00Kg
1682.05Kg
Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.
Horizontal component of the earth pressure Ph =
Vertical component of the earth pressure Pv =
Horizontal earth pressure force = 501.50
Lever arm x = M = 0.23mV
Eccentricuty e = b/2-x = 0.02m <b/6
Maximum stress = P/A(1+6e/b) = 4171.48 < SBC Hence O.K
Minimum stress = P/A(1-6e/b) = 2556.71 Hence O.K
Coefficient of friction between soil and footing u = 0.5
1.51 >1.25
Factor of safety against overturning = 2.56 >1.5
Factor of safety against sliding =(uFx0.9W)/Ph =
DESIGN OF FACE WALL (BIT-I)
2.40m2.40m0.00m
1800Kg/Cum2400Kg/Cum
0.30m1.50m
3063.47
020
0.60m15000.0Kg/Sqm
2
sin(Q+q)sin(Q-b)
2462.40Kg/sqm
3050.65Kg/sqm
3215.43Kg/sqm
Lever arm about C Moment(Kg-m)
0.15 259.200.70 2419.201.10 2851.201.21 3875.931.65 2138.40
11543.93
Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.
1.16m -3532.658011.28
Hence O.K
Hence O.K
DESIGN OF FACE WALL (BIT-II)
1.80m1.80m0.00m
1800Kg/CumM15
Fe4152400Kg/Cum
0.30m1.20m
3063.47
02070Kg/Sqcm
2300Kg/Sqcm13
0.2830.9068.9740.60m
15000.0Kg/Sqm
2
sin(Q+q)sin(Q-b)
1846.80Kg/sqm
1906.65Kg/sqm
2009.65Kg/sqm
Lever arm about C Moment(Kg-m)
0.15 194.400.60 1166.400.90 1312.200.90 1816.841.35 1312.20
5802.04
Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.
0.91m -1727.434074.61
Hence O.K
Hence O.K
DESIGN OF FACE WALL (BIT-III)
1.20m1.20m0.00m
1800Kg/CumM15
Fe4152400Kg/Cum
0.30m0.80m
3067.41
02070Kg/Sqcm
2300Kg/Sqcm13
0.2830.9068.9740.60m
15000.0Kg/Sqm
2
sin(Q+q)sin(Q-b)
1101.60Kg/sqm
973.55Kg/sqm
894.24Kg/sqm
Lever arm about C Moment(Kg-m)
0.15 129.600.47 336.000.63 342.000.58 520.390.95 615.60
1943.59
Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.
0.65m -636.701306.89
Hence O.K
Hence O.K
DESIGN OF FACE WALL (BIT-IV)
0.80m0.80m0.00m
1800Kg/CumM15
Fe4152400Kg/Cum
0.30m0.50m
3076
02070Kg/Sqcm
2300Kg/Sqcm13
0.2830.9068.9740.60m
15000.0Kg/Sqm
2
sin(Q+q)sin(Q-b)
604.80Kg/sqm
501.50Kg/sqm
338.05Kg/sqm
Lever arm about C Moment(Kg-m)
0.15 86.400.37 70.400.43 62.400.36 122.850.65 280.80
622.85
Note:-Weight of soil on the toe is neglected on the assumption that,it is scoured.
0.49m -243.73379.12
Hence O.K
Hence O.K
Hydraulic design
Hydraulic Particulars:-
1.Maximum Flood Level 6.235
2.Ordinary Flood level 5.015
3.Lowest Bed level 3.965
4.Average bed slope 0.015200(1 in 1000)
0.050(As per table 5 of IRC:SP 13)
6.Bottom of deck proposed 5.165(MFL+Vertical clearence)
7.Road Crest level 5.645(Bottom of deck level+thickness of deck slab)
8.Width of carriage way 6.000
Discharge Calculations:-
I)Discharge calculations of stream:-
A) Area-Velocity Method:-
a)At the proposed bridge site(20m upstream):-
Maximum Flood level 6.235mSlope 0.01520Rugosity Coefficient 0.050
S.No Chainage R.L Depth of Average Distance Area Wetted flow depth of (m) (Sqm) perimeter(m) flow (m)
(m)
1 0 6.500 0.00 0.00 0.00 0.00 0.002 1 5.340 0.90 0.45 1.00 0.45 1.083 2 4.560 1.68 1.29 1.00 1.29 1.054 4 3.965 2.27 1.97 2.00 3.95 2.055 6 4.780 1.46 1.86 2.00 3.73 2.346 7 5.300 0.94 1.20 1.00 1.20 1.127 9 6.100 0.14 0.54 2.00 1.07 2.308 10 6.420 0.00 0.07 1.00 0.07 1.05
11.74 10.99
Hydraulic Radius R= Total area/Wetted perimeter = 1.07
Velocity V = 2.58m/sec
AXV 30.28Cumecs
5.Rugosity Coefficient(n)
1/nX(R2/3XS1/2)
Discharge =
b)At 300m upstream of the the proposed bridge site:-
Maximum Flood level 9.235mSlope 0.01520Rugosity Coefficient 0.050
S.No Chainage R.L Depth of Average Distance Area Wetted flow depth of (m) (Sqm) perimeter(m) flow (m)
(m)
1 0 9.450 0.00 0.00 0.00 0.00 0.002 1 8.290 0.95 0.47 1.00 0.47 1.083 2 7.720 1.51 1.23 1.00 1.23 1.054 4 7.500 1.73 1.62 2.00 3.25 2.055 6 7.650 1.58 1.66 2.00 3.32 2.346 8 8.250 0.98 1.28 2.00 2.57 2.207 10 9.050 0.18 0.58 2.00 1.17 2.308 13 9.370 0.00 0.09 3.00 0.28 3.20
12.29 14.22
Hydraulic Radius R= Total area/Wetted perimeter = 0.86
Velocity V = 2.23m/sec
AXV 27.41Cumecs
c)At 300m downstream of the the proposed bridge site:-
Maximum Flood level 4.035mSlope 0.01520Rugosity Coefficient 0.050
S.No Chainage R.L Depth of Average Distance Area Wetted flow depth of (m) (Sqm) perimeter(m) flow (m)
(m)
1 0 4.400 0.00 0.00 0.00 0.00 0.002 1 3.240 0.79 0.40 1.00 0.40 1.083 2 2.460 1.58 1.19 1.00 1.19 1.054 4 1.660 2.38 1.98 2.00 3.95 2.055 6 1.770 2.27 2.32 2.00 4.64 2.346 8 3.200 0.84 1.55 2.00 3.10 2.207 10 3.750 0.29 0.56 2.00 1.12 2.308 13 4.320 0.00 0.14 3.00 0.43 3.20
14.82 14.22
Hydraulic Radius R= Total area/Wetted perimeter = 1.04
Velocity V = 2.53m/sec
AXV 37.49Cumecs
1/nX(R2/3XS1/2)
Discharge =
1/nX(R2/3XS1/2)
Discharge =
B) CATCHMENT AREA METHOD:-
Catchment area from stream alignment and local enquiry(Indicated in the drawing) = 1.38sqkm
21.65Cumecs
Design discharge of the stream = 30.28Cumecs
II)Discharge from surplus wier of tank:-
Assume head of flow = 0.45m (As enquired from local people)
Length of check dam = 22.75m
The discharge per metre length of check dam is calculated as given below:-
24.13Cusecs 0.68Cumecs
(Where Cd =4.10 as being adopted by Irrigation authorities )
Hence the total discharge over the check dam = Q2 = 15.47Cumecs
Design Discharge = 45.75Cumecs
Design Velocity = 2.58m/sec
Ventway Calculations & fixation of RTL:-
provide a vent area of about 40 percent but not less than 30 percent of the unobstructed area of the stream measured between the proposed road top level and the stream bed.However, the available area of flowunder design HFL condition should always be at least 70 percent of the unobstructed area of flow between the design HFL and the stream bed i.e. the obstruction under design HFL condition should not be more than 30per cent.
Trial 1:-
Assume RTL of +5.645m,the unobstructed area of the stream measured between the RTL andstream bed (from graphical calculation in AUTOCAD) = 66.53sqm
To avoid debris and other tree logs etc.getting clogged in the vents,it is proposed to provide 6mspans,for which open expansion joints are sufficient.Hence,3 spans of each 6m are proposed.Further 4Nos of 900mm dia are proposed on each side of the spans to avoid concentration of flow in the middle portion,thereby avoiding the formation of eddies and scouring of face walls.
Vented area available for middle span = 6.88sqm
---do---- for left side span = 5.75sqm
---do---- for right side span = 5.95sqm
Cumulative area of vents available from = 7.63sqm900mm dia pipes
Total vented area provided = 26.21sqm
Percentage of vented area provided = 39.40% >30%
Using Dicken's formula Discharge Q = CA3/4 =
q = Cd L h3/2. =
As per caluse 5.1.3(ii)a of IRC SP:82-2008,low level submersible structures like causeways,
Hence O.K
From local enquiry,the HFL is fixed as +6.235m
Total area between HFL and stream bed for defined cross section = 79.33sqm(from graphical calculation in AUTOCAD)
Area available for flow in between HFL and RTL/PBL = 30.06sqm
Total vented area provided = 26.21sqm
Hence.total area available, when the flow is at HFL = 56.27sqm
Percentage of obstruction = 29.07% <30%
Hence O.K
Afflux Calculations(H.F.L Condition):-
Un obstructed area of cross section = A = 79.33Sqm
Total vented area provided = a = 56.27Sqm
Design discharge Q = 45.75Cumecs
Linear water way L = 28.80m
0.80m
Width of the channel at HFL = 45.38m
Using Orifice formula for calculation of discharge
In the present case,
a/A = 0.71
0.867Corresponding to this value the coefficient e from IRC SP:13--2004 = 0.91
Hence
0.2673499 = h+ 0.09734964322
At just upstream of the bridge
1.0081534 = (0.80+h) X u
u = 1.00815337153 ----------------(2)(0.80+h)
Substituting,the above value in eq (1) '2
0.2673499 = h+ 0.097350 X 1.008153
Depth of down stream water Dd =
Case(a) Assume that afflux is less than 1.4Dd:-
Q = Co X (2g)1/2 X L X Dd X [h+(1+e)u2/2g]1/2
Corresponding to this value the coefficient Co from IRC SP:13--2004 =
u2 ------------- (1)
Q = W X (Dd + h) X u
(0.80+h)
Solving by trial and error method,assume h = 0.30m
0.267350 = 0.33376490624426 Not satisfied
assume h = 0.131m
0.267350 = 0.26776523434566
Hence afflux h = 0.131m
Velocity u = 1.083m/sec
Applying Broad crested wier formula,
0.94
Hence H = 0.99m
0.99m
u = 1.018m/sec
0.937
0.137
From the above calculations,it is inferred that afflux is less than 1/4 th Dd and hence afflux to be adopted is from the Orifice formula,which is equal to 0.131m
Scour Depth Calculations:-
As per the clause 101.1.2 of IRC:5--1985,the design discharge should be increased by 30% to ensure adequate margin of safety for foundations and protection works
Hence,the discharge for design of foundations = 1.30XDesign Discharge = 60.85Cumecs
2.00
Discharge per metre width of foundations = q = 2.113
1.75m
2.63m(For design of abutment foundations,as per clause 110.1.4.2 of IRC:5--1985)
Case(b) Assume that afflux is more than 1.4Dd:-
Q = 1.706 CW LH3/2
As per clause 15.2 of IRC SP:13-2004,the value of CW for narrow bridge opening with or without floor =
H = Du + u2/2g ≈ Du
Du =
Again applying Q = Du x W x u
Du = H - u2/2g
Hence, Du =
Hence afflux h = Du - Dd =
Lacey's Silt factor ' f ' = 1.76Xm1/2(Due to pebbles&boulders in the bed) =
Normal scour depth D = 1.34(q2/f)1/3 =
Maximum scour depth Dm = 1.5XD =
3.83m
Bottom level of foundation = 2.41m
Depth of foundation below low bed level = 1.56m
The Minimum Safe Bearing capacity of the soil is considered as 15 KN/m2 at a depth of 1.50m below LBL
Hence open foundation in the form of individual footings is proposed at a depth of 1.80m below LBL,ie,at a level of +2.315m
As the foundations are proposed below the Max.scour level,bed protection is not needed from scour depth considerations.
Design of Protection works:-
Afflux = 0.131m
Depth of flow = 2.27m
Head due to velocity of approach = 0.303m
Combined head due to Velocity of approach and 0.434mafflux
2.63m/sec
Linear water way required 7.67m <28.80m
Area available for flow at H.F.L = 56.27sqm
As per the clause 6.4.2(i),of IRC SP:82-2008,the post construction velocity under the structure should not exceed
protective works.
2.00m/sec
Discharge,that can be passed over the causeway safely = 112.54Cumecs >60.85
Hence O.K
As per the clause 5.1.3(iv),of IRC SP:82-2008 for the beds consisting of boulders upto 200mm size,the permissible velocity through vents is 2.5m/s and for beds containing larger sized boulders or rocky strata permissible velocity is 6m/s.
As the bed of the proposed stream is rocky strata,increased velocity of 2.68m/sec is allowed through vents withoutrigid floor protection.Hence rigid floor protection is not proposed.
However,suitably designed flexible aprons with cut-off walls are proposed on both upstream and down stream sides to protect against the probable eddies formed due to uneven spacing of vents along the causeway.
Design of cut-off walls/Toe walls:-
Though,it is sufficient to take the D/S side cut-off upto 1.27 times the normal scour depth as per caluse 703.2.3.2 of IRC 78-1983 considering that the reach is straight.
1.27XNormal scour depth from HFL = 2.22m
Depth of foundation = Dm + Max.of 1.2m or 1/3 Dm =
di =
(Vmax2/2g)X[di/(di+x)]2
hi =
Velocity through vents Vv = 0.90X(2ghi)1/2 =
LWW = Qd/(VvXdi) =
2 m/s and the intensity of discharge is limited to 3m3/m except in the case of properly designed raft foundation with adequate
Hence Vlim. =
Depth of bottom of Cut-off wall from HFL = 2.22m
Bottom level of cut-off wall = 4.01
Depth of bottom of D/S side Cut-off wall from LBL -0.05m
As per the clause 6.4.2(v),of IRC SP:82-2008,the minimum depth of cut-off wall on U/S side is 2.0m below bed level and 2.5m below bed level on D/S side.
Depth of bottom of D/S side Cut-off wall from LBL 2.50m
Depth of bottom of U/S side Cut-off wall from LBL 2.00m
As rigid floooring is not being proposed,there is no need to provide cut-off walls.But toe walls are proposed to a depth of 0.90m to protect the flexible apron.
Design of LAUNCHING/FLEXIBLE APRONS:-
Size of stones as per clause 5.3.7.2 of IRC 89-1985
0.28mSay 0.30m
Weight of each stone considering the specific gravity of stone as 2.65
37.48Kg
Say 40Kg
Weight of each stone shall not be less than 40 Kg.
Dimensions of apron as per clause 5.3.5.2 of IRC 89-1985
0.236
Thickness of apron at inner edge(near raft) = 1.5 x T = 0.354m
Say 0.60m
Thickness of apron at outer edge = 2.25 x T = 0.531m
Say 0.90m
Hence provide a thickness of 0.60m at near end and 0.9m at the outer end
Width of Launching Apron on U/S Side:-
The launching aprons are designed to reach a level of 1.50 times the normal scour depth
1.5 x D = 2.625m
Bottom level of apron after launching = HFL-1.5 X D = 3.61m
Depth below top of the raft = -1.65m
The apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89
Hence the width of launching apron at U/S = -3.30m
Diametre (d) = (Vmax/4.893)2 =
Weight of stone =4/3x x(d/2)3 x 2.65 x 1000 =
( T ) = 0.06 x (Qdf)1/3 =
As per the clause 6.4.2(vi),of IRC SP:82-2008,minimum width = 4.0m
Width of Launching Apron on D/S Side:-
The launching aprons are designed to reach a level of 2.00 times the normal scour depth
2.0 x D = 3.500m
Bottom level of apron after launching = HFL-2 X D = 2.74m
Depth below top of the raft = 0.23m
The apron should launch in a slope of 1V : 2H as per clause 5.3.7.6 of IRC 89
Hence the width of launching apron at D/S = 0.46m
As per the clause 6.4.2(vi),of IRC SP:82-2008,minimum width = 6.0m