Design Of Bridge Pier 5q5l2h

Design parameters :

Design of R.C.C. Bridge Piers of Ladpura Bridge on RMC

Canal discharge Q =

188.45

Clear span between piers = Thickness of road way deck slab = F.S.L. of canal U/S of Bridge = F.S.L. of canal D/S of Bridge = Canal bed Level D/S of Bridge = Lacey's Silt factor (f) =

8.00 0.8 256.42 256.42 253.22 1.00

m m

Bearing Capacity of Soil = Width of roadway slab of bridge = Width of Kerb on roadway bridge = Thickness of Kerb = Weight of Railing per m run of bridge = Eccen of C/L road deck slab from pier center= Height of Pier upto Bed block top LVL from CBL = Thickness of Bed block = Area of bridge Hoisting platform = Width of pier Length of pier at bed block bottom level = Length of pier at CBL = LVL of wearing top of road way deck slab = LVL of deck slab bearing LVL of top of foundation block of Pier No of bays of bridge Length of Pier at FSL D/S of bridge Length of Pier at CBL D/S of bridge Length of foundation block at foundation LVL Width of foundation block at foundation LVL Height of foundation block at Pier-footing junct Height of foundation block at edge of footing (i) Foundation Level of Piers Normal depth of scour (R) =0.47(Q/f)1/3

25 3.5 0 0 0.7 0 4.1 0.6 0 1.5 5 5.3 258.22 257.32 253.22 3 5.03 5.3 7.5 4 1.5 1

t/m2 m m m ton/m m m m m2 m m m m m m Nos m m m m m m

Anticipated depth of scour around piers = 1.5 ( R ) =

cumecs

m m

2.69

m

4.04

m

Level of foundation of Piers should not be less than 1 m below anticipated depth of scour Level of foundation = 251.38 m say 251.70 m

Evaluation of forces acting on the Pier (a) Dead weight of super structure (i) Weight of slab with wearing coat = (iii) Weight of Railings = Total

66.50 13.30 79.80

tonnes tonnes tonnes

(b) Live Loads Maximum live load reaction on pier is obtained when fourth axle load 11.4 t at center of pier

(i) Reaction from right span = 16.70 (ii) Reaction from left span = 12.55 Total Live Load reactio on the Pier from live loads = Impact Factor = 0.29 So Maximum live load reaction with impact = 37.82 Eccentricity of live load eccentricity of L.L. from center of pier about Y-Y axis = eccentricity of L.L from center of pier about X-X axis =

tonnes tonnes 29.24

tonnes

tonnes 0.55 0.11

m m

(c) Braking Force It is equal to 20% of total live load present on the bridge = Reduced level of application of braking force = Height of appication force above bearing level = Increase in reaction due to braking force = 1.85

8.36 259.42 2.100 tonnes

tonnes m m

(d) Temperature force due to sliding friction Reaction on sliding end when loads are placed so as to produc maximum reaction at sliding end Live load Reaction at sliding end = 14.32 tonnes Impact factor = 0.29 Live load with impact = 18.51 tonnes Dead Load reaction = 79.80 tonnes Increase due to braking force = 1.85 tonnes Total : 100.45 tonnes Friction in sliding bearing ( with coeff. of sliding friction as 0.03) = 3.01 tonnes R.L. of point of application = 257.32 m

(e) Wind force Since intensity of wind pressure depends upon the height of the point above mean retarding surface, so two cases for calculation of wind forces have been considered (i) When level of water in the canal is at F.S.L. (ii) When depth of water is zero (i) When level of water in the canal is at F.S.L. Average height of elevation area =

1.80

Intensity of wind pressure =

46.3

Exposed Elevation area = Total Wind force on structure = R.L. of point of application =

17.10 0.79 257.32

Wind force on live load Intensity of wind force = Length of live load = length of one span = Total wind force on live load = R.L. of point of application =

300.00 9.50 2.85 259.42

(ii) When depth of water is zero Average height of area of elevation above bed level =

m kg/m

2

m2 tonnes m

kg/m m tonnes m

5.00

m

Intensity of wind pressure = Exposed Elevation area = Total wind force on structure = R.L. of point of application =

85.0 47.5 4.04 255.72

kg/sqm sqm tonnes m

Wind force on live load Total wind force on live load = R.L. of point of application =

2.85 259.42

tonnes m

Sqm m 15.93

tonnes

Dead load of pier =

23.10

tonnes

(iii) Force due to buoyancy Plan area at F.S.L. = Weight of Water displaced = Force due to buoyancy allowing 15% upward force =

6.60 21.12

Sqm tonnes 3.17

(f) Dead Loads of Sub Structure (i) Dead Load of bed block Plan area = Thickness = Weight of bed block =

10.62 0.6

(ii) Dead Load of pier

(g) Force on pier due to current of water Maximum Velocity of flow (V) = Q/PR =

2.45

tonnes

m/s

V= 6.02 Maximum value of depth of scour = 1.5 R = 4.04 m Assuming variation of V2 to be linear than its value at bed level = 2

Pressure due to water current = K V2

where K =

26

Pressure at water level =

156.56

kg/m

Pressure at bed level = Area on which pressure acts = Total force due to water current = Height of center of pressure from bed level =

32.61 4.80 0.45 1.95

kg/m2 Sqm tonnes m

2

(h) Force on pier due to current of water perpendicular to length of pier Maximum variation in direction of current = 20 0 Maximum Velocity at top = V sin 20 =

0.84 V2=

Value of V2 at bed level = Assuming K =

80

0.70

0.02 for rectangular shape

Pressure at water level =

56.30

kg/m2

Pressure at bed level = Area on which pressure acts =

1.27 16.48

kg/m2 Sqm

1.25 for pointed Nose 45 degree angled

Total force due to water current = Height of center of pressure from bed level =

0.47 2.11

tonnes m

(i) Force on pier due to pressure of water perpendicular to length of pier when water flows in alternate bays Lateral Forces on pier when one gate is opened for flow and adjacent one are closed F = g `h A `h = 1.61 m Area under influence for water pressure = 14.13 sqm Total pressure force F = g `h A = 22.80 tonnes Center of pressure below water surface y p =( I0/A`h ) +`h I0= h3(a2+4ab+b2)/36 a b=

5.46

yp =

1.85 Level of center of pressure above base =

m3

m 254.566 m

Check for stresses in the pier at Bed Level with R.L. = Area (A) = Ixx=

6.83

Sqm

Iyy=

1.17

m4

12.16

m4

253.22

m

Case 1 : When Live load on the bridge and canal is running at F.S.L. (i) Vertical dead loads (a) Dead Load of super structure = (b) Dead load of bed block = (c) Dead Load due to self weight of Pier = (d) Increase in reaction due to braking = (ii) Live load with impact factor = (iii) Buoyancy force acting upwards =

79.80 15.93 23.10 1.85 37.82 -3.17

So Net vertical downward force (P) =

155.33 tonnes

Moment about x-x axis Due to braking force = Due to sliding friction = Due to water current in perpendicular direction = Due to water pressure when alternate gates open = Total Moment (Mx) = say Moment about y-y axis Due to eccentricity of Live Load = Due to wind force on super structure = Due to wind force on live load = Due to water current force in long. Dir = Total Moment (My) = say Now stress =

tonnes tonnes tonnes tonnes tonnes tonnes

51.83 12.36

t.m t.m 1.00 30.70

95.89 96.00

t.m t.m

20.80 3.25 17.67 0.89 42.60 43.00

t.m t.m t.m t.m t.m t.m

90.26

t/m2

t.m t.m

My P Mx  ( xm )  ( ym ) A I xx I yy

Maximum compressive stress σ com,max=

< 250 t/m2

Minimum compressive stress σ com,min=

-45.27

t/m2 =

-0.453

N/mm2

However steel provided in pier will take care of tension.

Case 2 : When Live load on the bridge and No water in canal (i) Vertical dead loads (a) Dead Load of super structure = (b) Dead load of bed block = (c) Dead Load due to self weight of Pier = (d) Increase in reaction due to braking = (ii) Live load with impact factor =

79.80 15.93 23.10 1.85 37.82

So Net vertical downward force (P) =

tonnes tonnes tonnes tonnes tonnes

158.50 tonnes

Moment about x-x axis Due to braking force = Due to sliding friction = Total Moment (Mx) = say

51.83 12.36 64.19 65.00

t.m t.m t.m t.m

say

20.80 3.25 17.67 41.72 42.00

t.m t.m t.m t.m t.m

Maximum compressive stress σ com,max=

73.89

t/m2

Minimum compressive stress σ com,min=

-27.44

Moment about y-y axis Due to eccentricity of Live Load = Due to wind force on super structure = Due to wind force on live load = Total Moment (My) =

Now stress =

My P Mx  ( xm )  ( ym ) A I xx I yy (Tensile) t/m2 =

N/mm2

< 250 t/m2 -0.274

N/mm2

251.70

m

However steel provided in pier will take care of tension.

Check for stresses in the pier at foundation Level with R.L. = Area (A) = Ixx=

30.00

Sqm

Iyy=

40.00

m4

140.63

m4

Case 1 : When Live load on the bridge and canal is running at F.S.L. (i) Vertical dead loads (a) Dead Load of super structure = (b) Dead load of bed block = (c) Dead Load due to self weight of Pier = (d) Increase in reaction due to braking = (e) Live load with impact factor = (f) Buoyancy force acting upwards = (g) Dead load of foundation block =

So Net vertical downward force (P) =

79.80 15.93 23.10 1.85 37.82 -3.17 98.02

tonnes tonnes tonnes tonnes tonnes tonnes tonnes

253.34 tonnes

Moment about x-x axis Due to braking force = Due to sliding friction = Due to water current in perpendicular direction = Due to water pressure when alternate gates open = Total Moment (Mx) = say Moment about y-y axis Due to eccentricity of Live Load = Due to wind force on super structure = Due to wind force on live load = Due to water current force in long. Dir = Total Moment (My) = say Now stress =

64.54 16.94

t.m t.m 1.71 65.36

t.m t.m

148.55 149.00

t.m t.m

20.80 4.45 22.00 1.57 48.82 49.00

t.m t.m t.m t.m t.m t.m

17.20

(Compressiv e) t/m2 < 25 t/m2

My P Mx  ( xm )  ( ym ) A I xx I yy

Maximum compressive stress σ com,max= Minimum compressive stress σ com,min=

-0.31

-0.003

t/m2 =

Case 2 : When Live load on the bridge and No water in canal (i) Vertical dead loads (a) Dead Load of super structure = (b) Dead load of bed block = (c) Dead Load due to self weight of Pier = (d) Increase in reaction due to braking = (e) Live load with impact factor = (f) Dead Load of foundation block =

79.80 15.93 23.10 1.85 37.82 112.50

So Net vertical downward force (P) =

271.00 tonnes

Moment about x-x axis Due to braking force = Due to sliding friction = Total Moment (Mx) = say Moment about y-y axis Due to eccentricity of Live Load = Due to wind force on super structure = Due to wind force on live load = Total Moment (My) =

My P Mx  ( xm )  ( ym ) A I xx I yy

t.m t.m t.m t.m

20.80 4.45 22.00 say

Now stress =

64.54 16.94 81.48 82.00

tonnes tonnes tonnes tonnes tonnes tonnes

47.25 48.00

t.m t.m

t.m t.m t.m

N/mm2 O.K.

Maximum compressive stress σ com,max= Minimum compressive stress σ com,min=

14.41 3.65

t/m2 t/m2 =

< 25 t/m2 0.037

N/mm2

Area of steel 0.3% of gross sectional area as per IRC 21 Provide 20 mm dia main reinforcement at spacing of 190 mm with ties bar 12 mm dia 200 mm c/c

O.K.

ernate bays

Design of Reinforcement for foundation Block of Ladpura Bridge of RMC : Bearing capacity of Soil/Rock : Angle of internal friction of soil mass F:

25 30.0

kN/m2 degree

Unit Weight of soil : Coefficient of friction between soil and concrete :

18.0

kN/m3

Concrete Grade M 20 with σcbc :

6.7

0.5 N/mm2

Steel of Grade Fe 415 with σst

230.0 N/mm2 Design constants : For M 30 concrete and Fe 415 steel reinforcement we have the following : Modular ratio m =280/3σcbc= 14.00 Kbal=1/(1+(σst/mσcbc))=

0.289

jbal=1-kbal/3

0.904

Rc=0.5σcbckbaljbal=

0.870

Ka= (1-sinF)/(1+sinF)=

+X

4

0.333 C A Consider dimensions of footing to be checked : Length of column in x-x dir = 5.3 m Width of column in y-y dir = 1.5 m Length of footing base in x-x dir 7.5 m Width of footing base in y-y dir 4 m -Y Moment about x-x direction = 1490.00 kN.m +Y Moment about y-y direction = 490.00 kN.m 7.5 Vertical load on column = 2533.43 kN 5.3 Maximum soil pressure at toe = 172.01 kN/m2 Minimum soil pressure at heel = -3.12 kN/m2 Pressure intensity under column axis = 84.45 kN/m2 Intensity of soil pressure below the column face = 146.328 kN/m2 Cantilever length for bending about critical face = 1.10 m Total force under cantilever length = 700.353 kN D B Distance of centroid about critical face = 0.51 m 1.5 Bending moment about critical face = 359.59 kN.m Width of section at crtical face 1.813 m -X Depth of footing base as required from bending consideration = 477.64 mm Provide depth of footing base as 900 mm AS PER SCOURING DEPTH CRITERION AND IRC 21 DESIGN CRITERION Effective cover of reinforcement 60 mm Total depth of footing base at column face = 960 mm Provide total depth of footing base at end = 500 mm

Check for Shear Force (a) Punching Shear force : For punching shear stress point of view the crritical section occurs at distance d/2 from coloumn face. Position of critical face = 450 mm from coloumn face Eff. Length of critical plane for punching shear stress = 5.75 m Eff. Width of critical plane for punching shear stress = 1.95 m

Punching shear force (F) = 1586.56 kN Depth of section at punching shear line of influence = 0.7344 m Punching shear stress at section for critical punching shear force= 140.282 kN/m2 Permissible shear stress in punching shear = ks x 0.16 Öfck = 715.54 kN/m2 The section is safe from punching shear point of view O.K. (a) One way Shear force : For one way shear stress point of view the critical section occurs at distance d from column face. Position of critical face for oneway shear = 900 mm from column face Cantilever length to right of critical plane = 0.2 m Intensity of pressure at critical plane = 167.344 kN/m2 The section at critical plane will be trapezoidal with Top width of trapezoid = 3.5454545455 m Effective depth of critical sectio 523.6363636364 mm Depth of Neutral Axis = kd' = 151.15 mm Width of section at neutral axis level = 4.367 m Shear force at critical section = 135.74 kN Shear stress at crtical section = 0.227 N/mm2 Permissible shear stress at section due to direct shear= 0.28 N/mm2 Section is safe in direct shear O.K. Design for bending Tension : Area of steel required for bending (Ast) = 1922.12 mm2 Area of steel wire 16 mm dia = 200.96 mm2 No of bars required for bending 10 Nos Provide 16 mm dia HYSD bars at spacing @ 400.0 mm c/c However provide 16 mm dia bars at spacing 200.0 mm c/c at bottom of footing Provide same spacing of bars in other direction also. Also provide 12 mm HYSD bars @ 200 mm c/c for temp/shrinkage on top face of foundation block.