Bridge Pier

DESIGN OF WELL CAP

Centre to centre of pier  RBL Bed level of canal Hard rock level; Thickness of pier at top Sode slope of the pier  Base width Width of the trough Depth of flow of water  Thickness of bed slab of trough Ground level Top of deck slab of catwalk Thickness of bearing Thickness of bed block/pier cap  Assume thickness of well cap= Size of the base Bottom of deck slab Top of bed block level Bottom of bed block Height of pier  Horizontal seismic coefficient Deepest bed level Thickness of steining Pier length below corbel

20.00 m 551.00 m 570.00 m 549.50 m 1.20 m 12V:1H 2.53 m 5.55 m 4.80 m (including surge) 0.75 m 560.00 m 575.65 m 0.50 m 0.75 m 1.25 m 2.53 2. 53m m X 5.0 5.00m 0m 569.25 m 568.75 m 568.00 m 8.00 m 0.08 g 549.50 m 0.70 m 5 m

1

2. TENTATIVE SECTION OF THE PIER 575.65m V1=343.93t

V1=343.93t

on each bearing V1=

H=37.22T .50m

1.20m 1

1

12

12

h

V2=191.446t 2.53m 560.00m D

551.00m

2

5.00m

Myy

+VE +VE

2.53m

+VE

Mxx

3

3. EVALUATION OF FORCES: a)Dead load of super structure R.L.of section under consideration SL.NO. DESCRIPTION OF LOAD I TROUGH PORTION 1 Weight of side beams 2 Weight of fillets 3 Weight of chamfers 4 weight of bed slab 5 Weight of bottom stiffener 6 Weight of top stiffener 7 Weight of top wedge/ext beam 8 Weight of side stiffener 9 Weight of cat walk beam 10 Weight of cat walk slab 11 Weight of water 12 weight of wearing coat 13 Weight of railing 14 Live Load 15 Add for unforseen loads TOTAL II PIER CAP 1 pier cap III 1 2

PIER weight of corbel portion Weight of pier

III 1

FOUNDATION Well cap

560.00 m NO.

V(t) 2 2 2 1 6 6 6 6 1 1 1 1 6 1 5%

20.00 20.00 20.00 20.00 0.50 0.50 20.00 0.70 20.00 20.00 20.00 20.00 20.00 20.00

X X X X X X X X X X X X X X

1.00 1.50 0.65 2.50 4.00 5.50 0.40 2.19 0.30 0.90 5.50 1.65 0.25 1.20

X X X X X X X X X X X X X X

4.02 0.78 1.21 0.45 0.65 0.75 0.35 0.50 0.75 0.20 4.80 0.08 0.25 1.00

X X X X X X X X X X X X X X

2.40 2.40 2.40 2.40 2.40 2.40 2.40 2.40 2.40 2.40 1.00 2.40 0.79 1.00

385.92 111.60 75.63 54.00 18.72 29.70 40.32 11.06 10.80 8.64 528.00 5.94 5.89 24.00 65.51 1375.72

1

1.80

X 8.00

X 0.75

X 2.40

25.92

1 1

1.18 1.87

X 5.15 X 5.00

X 2.00 X 7.25

X 2.40 X 2.40

29.05 162.40

1

3.14

X 8.41

Total with well cap Total without well cap

4

X 1.25

X 2.40

transition

1500

125.25721 15.967145

93.482906 3500

217.37

432

79.26

216.22

79.26 1672.35 1593.09

2148.22

1.5 ah

Earthquake forces

   H

H=

15.65

SL.NO. DESCRIPTION OF LOAD

seismic factor

h

NO.

m I 1 2 3 4 5 6 7 8 9 10 11 12

TROUGH PORTION Weight of side beams Weight of fillets Weight of chamfers weight of bed slab Weight of bottom stiffener Weight of top stiffener Weight of top wedge/ext beam Weight of side stiffener Weight of cat walk beam Weight of cat walk slab weight of wearing coat Weight of railing

II

TOTAL PIER

1 2 3

pier cap weight of corbel portion Weight of pier

III 1

FOUNDATION Well cap

1 2 2 1 6 6 2 2 1 1 1 6

1 1 1

1

11.65 16.20 12.75 16.53 15.98 15.40 15.28 14.86 15.43 15.55 15.55 16.25

0.09 0.12 0.10 0.13 0.12 0.12 0.12 0.11 0.12 0.12 0.12 0.12

16.03 14.65 10.03

0.12 0.11 0.08

0.50

0.00

total 5

He m

Ve t 34.47 13.86 7.39 6.84 2.29 3.51 4.72 1.26 1.28 1.03 0.71 0.73

17.24 6.93 3.70 3.42 1.15 1.75 2.36 0.63 0.64 0.52 0.35 0.37

78.10

39.05

3.18 3.26 12.48

1.59 1.63 6.24

18.93

9.47

0.30 0.30

0.15 0.15

97.339

48.670

L1 m 11.65 16.20 12.75 16.53 15.98 15.40 15.28 14.86 15.43 15.55 15.55 16.25

16.03 14.65 10.03

0.50

L2 m 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.40 1.60 2.50 1.60

1.6 2.50 2.50

2.50

M1 t-m

M2 t-m

401.62 224.57 94.27 113.07 36.63 54.01 72.14 18.71 19.70 16.02 11.01 11.92

43.09 17.33 9.24 8.55 2.87 4.38 5.90 1.57 1.53 0.82 0.89 0.59

1073.68

96.77

51.04 47.80 125.15 223.99

2.55 4.08 15.60 0.00 22.23

0.15 0.1519407

0.38 0.38

1297.818

119.383

Y1= X1=

2.45 26.67

ey= ex=

HYDRODYNAMIC FORCES (trough)

He

C  ì ï y æ   y ö  y æ   y ö üï C s = m í ç 2 - ÷ + ç 2 - ÷ý 2 ï î h è  h ø h è  h ø ïþ Horizontal hydrodynamic force=He=0.726pe y

  y

2 

Moment about C.G=Me=0.299p e  y 

   h

y [m] h[m]

4.80 12.40

i  Dueto upstream water 

a= Cm= Cs= pe= He= Me=

21.337

100%

o

0.570 0.403 0.400 t/sq.m 27.88 t 55.12 t-m

6

-1.186265 m -24.16586 m

Dynamic force in the longitudinal direction in the trough Discharge in the trough(max) Cross sectional area of flow= Perimeter of the flow of water in the trough Kinematic viscocity= Flow velocity Reynolds No. Drag Coeffcient Drag force Hydraulic mean depth Shear force due to water/m length= Total force R.L. of application of force Height above the bed block= Increase in reaction due to drag force=

47.25 cumec 26.640 sq.m 15.150 m 1.14E-06 sq.m/sec 1.77 m/s 7500 0.123 37.22 t 1.758 m 1.758 kg 0.533 t 578.050 m 10.050 m 37.221 t

Force due to sliding friction: Reaction sliding end when the loads are so placed as to produce maximum reaction on the other end

L.L reaction= Impact factor Impact load

24.00 t 25.00% 6.00 t

Impact load Dead load reaction Load due to water in flow direction force Friction in sliding (Coeff of friction= R.L. of point of application of force

6.00 41.27 37.22 84.49 21.12 568.00

0.25

7

t t t t t m

Wind force The inensity of wind pressure depends on the height of structure exposed to the wind. Two cases are dealt for computing wind force (a). When level of water in the river is at HFL (b). When there is minimum water level  Average height of pier above GL=  Area of exposed structure

8.00 m 148.27 sq.m

Height of pier above GL= Intensity of wind pressure  Area of exposed structure  Add for catwalk area Total area= Total wind force on the structure= l1 l2 y= RL of point of application

10.00 121.77 148.27 30.00 178.27 21.71 6.40 3.60 5.713 565.71

8

m kg/sq.m sq.m sq.m sq.m t m m m

MOMENT OF INERTIA OF PIER AT BASE:  Area of the base B= L=

2

 A = B x L =

=12.67 m

M.I. Of the foundation:  I  x  I  y

Coeff. Friction at the bearings=

 LB -

 x

 y

3

=

4

=6.77 m

12

 BL -

2.533m 5.000m

=

3

4

=26.39 m

12

0.90 Y

1

2 X

X

B

4 Y

3

L

9

DETAILS

SL.NO

1

LOAD

DEAD LOAD

t 1593.09

-do- dry CONDITION

1065.09

5

FORCE DUE TO SLIDING FRICTION

6

WIND FORCE

13

EARTQUAKE FORCES

14

HYDRO DYNAMIC FORCES

HX

Hy

t

t

21.71

97.34 27.88

10

X

t/sq.m m 125.77 negligible

BENDING STRESS  (fx) t/sq.m

BENDING STRESS  (fy) t/sq.m

84.09 21.12

-48.67

DIRECT STRESS

97.34

8.00

31.60

0.00

16.21

0.00

33.34

0.00 222.56 10.31

112.77

-3.84 as above

5.22

CASE

Sf y

1

STATIC & DRY CONDITION

2

STATIC & WHEN THERE IS WATER ( IN TROUGH)

1593.091

21.707

21.123

125.770

0.000

-33.341

124.03

190.71

127.51

4

dirction of eq. along flow CASE(1)+E.Q(NO. W IND FORCE)

1016.421

97.339

118.462

80.244

0.000

46.084

302.81

302.81

-142.32

5

CASE(2)+E.Q(NO. WIND LOAD)

1544.421

125.224

118.462

121.928

10.307

51.306

386.39

386.39

-142.54

6

dirction of eq along the bridge CASE(1)+E.Q(NO. WIND FORCE)

1016.421

97.339

118.462

80.244

0.000

46.084

-32.52

193.01

226.35

1544.421

125.224

118.462

121.928

10.307

51.306

51.07

276.60

276.60

-32.521 386.395

117.427 386.395

-142.539 276.597

CASE(2)+E.Q(NO. WIND LOAD) dirction of eq across thebridge

Hx t 21.707

Sf x

V t 1065.091

7

CONDITION

Hy t

F/A t/sq.m 84.086

t/sq.m 0.000

t/sq.m -33.341

f1 t/sq.m 50.75

f2 t/sq.m 117.43

f3 t/sq.m 117.43

Min. stress Max. Stress max Tension= Max . Compress ion=

11

-142.539 t/sq.m 386.395 t/sq.m

Design of well cap: Diameter of well(internal) External dia Effective dia= Min of L+d or L+t depth assumed Intensity of loading=  Assuming well cap to be partially fixed moment, Moment at mid span= Grade of concrete Permissible stress in steel Permissiblebond stress= Permissible tensile strength in concrete= Whether with Earthquake considered(Y/N) Permissible compressive strength of concrete= m= k=  j= Q= Depth of well cap=

4.40 5.80 5.10 1.25 95.985

m m m m t/sq.m

78.018 M 1900.00 8.00 20

t-m 20 kg/sq.cm kg/sq.cm kg/sq.cm

7 N/mm2 13.3333 0.3294 0.8902 2

 Mx10 5 Qb

10.2634 bd 87.19 cm

Steel required at mid span & bottom of well cap (+ve moment) Dia of the bar 25 mm  Area 4.91 sq.cm Overall depth= 102.19 cm Say 125.00 cm Effective depth= 117.50 cm  Area of steel= 39.26 sq.cm 12.50 cm c/c Spacing= Say 125 mm c/c

12

Steel required at bottom in lateral direction(across width of pier) Moment= 39.009 Depth of well cap= 25.32 Dia of the bar 20  Area 3.142 Overall depth= 39.32 125 Say Effective depth= 117.5  Area of steel= 19.629 Spacing= 16.0 Say 150

t-m cm mm sq.cm cm cm cm sq.cm cm c/c mm c/c

Distance from face to of the support upto which radial reinforcement is to be provided Location of zero radial moment from centre=

 R

1.47 m

3

Therefore distance from support= Add for thickness=

1.43 m 2.13 m

This will be greater of the following 1. Ld=fs/4tbd =

148.44 cm

2. Point of inflection+d 3. Point of inflection+12f Maximum=

220.75 132.00 220.75 220

Say

cm cm cm cm

13

Area of reinforcement /width for -ve B.M. Mr at edges(radial rods)

Moment=

2 16

WR 2

78.018 t-m

Depth of well cap= Dia of the bar  Area Overall depth= Effective depth=  Area of steel= Spacing=

Say

25 4.909 125.00 120.00 38.439 12.770 125

mm sq.cm cm cm sq.cm cm c/c mm c/c

-142.54 -57.64 30.34 25.00 4.91 16.18 150.00

t/sq.m t sq.cm mm sq.cm cm c/c mm c/c

Column dowel reinforcement:

Tensile stress Tensile force=  Area of steel= Dia of the bar  Area Spacing=

Say

14

Distribution steel at top Dia of the bar ast=  Area of steel= @.12% of Ac Spacing Say

20 3.14 15 20.94

mm sq.cm sq.cm cm c/c 200 cm c/c

At the edge of slab, the mesh bars are free and are not capable of taking full tension. Therefore 20mm dia at 200 c/c circumferentail steel is provided for a length of up to 1.30m from the inner edge In the cntral region provide 20mm dia @ 200 c/c both ways Check for shear shear force= Shear stress % of steel= correction factor=

Permissible shear stress= Permissible Shear stress kt Balance shear

607.91 0.52 3.14 1.30

kN N/mm2 % k 2

0.44 N/mm 2 0.57 N/mm 2

- N/mm

15

PIER DESIGN -STRESS AT FOUNDATION CASE-6 (STRESS ES AT POINT1 & 2)

250.00

PIER DESIGN -STRESS AT FOUNDATION CASE-5. (STRESS ES AT POINT1 & 2)

200.00    )   m  .150.00   q   s    /    t    (100.00    S    S    E    R 50.00    T    S

   )   m  .   q   s    /    t    (    S    S    E    R    T    S

0.00

0

5.00

-50.00

450.00 400.00 350.00 300.00 250.00 200.00 150.00 100.00 50.00 0.00 0

BASE WIDTH(m)

5.00 BASE WIDTH(m)

PIER DESIGN -STRESS AT FOUNDATION CASE-7 (STRESS ES AT POINT1 & 2)

PIER DESIGN -STRESS AT FOUNDATION CASE-1 (STRESS ES AT POINT1 & 2)

140.00

300.00    ) 250.00   m  .   q200.00   s    /    t    (    S150.00    S    E100.00    R    T 50.00    S

120.00    ) 100.00   m  .   q   s80.00    /    t    (    S60.00    S    E    R40.00    T    S

20.00

0.00 0

BASE WIDTH(m)

0.00

5.00

0

16

BASE WIDTH(m)

5.00

PIER DESIGN -STRESS AT FOUNDATION CASE-2(@1 & 2)

250.00

PIER DESIGN -STRESS AT FOUNDATION CASE-3(@1 & 3)

350.00 300.00

200.00

   )   m  .250.00   q   s    /    t    (200.00    S    S150.00    E    R    T100.00    S

   )   m  .   q 150.00   s    /    t    (    S    S 100.00    E    R    T 50.00    S

50.00

0.00

0.00

0

BASE WIDTH(m)

0

2.53

PIER DESIGN -STRESS AT FOUNDATION CASE-1(POINT@1 & 3)

140.00

2.53

PIER DESIGN -STRESS AT FOUNDATION CASE-2 (STRESS ES AT POINT1 & 3)

128.00

120.00

BASE WIDTH(m)

127.00

   ) 100.00   m  .   q   s 80.00    /    t    (    S 60.00    S    E    R 40.00    T    S

   )   m  . 126.00   q   s    /    t    ( 125.00    S    S    E 124.00    R    T    S

20.00

123.00

0.00 0

BASE WIDTH(m)

122.00

2.53

0

17

BASE WIDTH(m)

5.00

PIER DESIGN -STRESS AT FOUNDATION CASE-4(POINT@1 & 3)

500.00

400.00

400.00    )300.00   m  .   q   s200.00    /    t    (    S    S100.00    E    R 0.00    T    S

-100.00

PIER DESIGN -STRESS AT FOUNDATION CASE-3(POINT@1 & 3)

300.00

0

-200.00

   )   m  . 200.00   q   s    /    t    ( 100.00    S    S    E 0.00    R    T    S

2.53

-200.00

BASE WIDTH(m)

PIER DESIGN -STRESS AT FOUNDATION CASE-5(POINT@1 & 3)

300.00

0

2.53

-100.00 BASE WIDTH(m)

PIER DESIGN -STRESS AT FOUNDATION CASE-5(POINT@1 & 3)

250.00 200.00

   ) 250.00   m  .   q200.00   s    /    t    (    S150.00    S    E100.00    R    T    S 50.00

   )   m  .   q150.00   s    /    t    (    S100.00    S    E    R 50.00    T    S

0.00 0

0.00 0

BASE WIDTH(m)

-50.00

2.53

18

2.53

BASE WIDTH(m)