Abutment

ABUTMENT

Design data ;

1. Deck level (top of w.c) = 477.740 m

2. H.F.L = 475.580 m

3. L.W.L = 474.700 m

4. Scour level = 474.154 m

5. Founding level = 472.554 m

6. S.B.C at founding level = 30.0 T/m2

o
o
7. Properties of backfill soil f= 30 d = 20.1

d dry
= 1.90 T/m3 d wet
= 1.00 T/m3

9. Seismic coefficients :-
Seismic forces are calculated as per cl. 219 of IRC:6-2017. The location falls in the zone V
of the seismic map. The importance factor has been considered as 1.2

Z= 0.36 ( From Table 16 of IRC:6-2017 corresponding to zone v)

I= 1.2 ( From Table 19 of IRC:6-2017 )

Sa/g = 2.5 (From footnote of IRC:6-2017 )

R= 3.0 ( Table 20 of IRC:6-2017 )

Horizontal Seismic coefficient as per relation given at page 50 of IRC:6-2017

A h = Z / 2 * I / R * Sa /g

= 0.36 / 2 * 1.2 / 3.0 * 2.5

= 0.180
Vertical Seismic coefficient = A h * 2 / 3 = 0.12
(cl. 219.3 of IRC:6-2017)
 Abutment

RL 477.740
200

200
200
RL 476.834
500

600 HFL = 475.58 m

Scour level
824 474.55 m

RL 473.15

600 600
400 RL 472.55
X RL

2400 1000 2000

 Abutment

150 150

200

1000 12000

350
150 150

Load from Superstructure

A) Dead Load
From design of superstructure
Reaction on each side = 150.0 T ( Refer design of superstructure )

B) Live Load Reaction on Abutment

Refer Table 6 & 6A bridge has to be designed for
I) One lane of class 70 R + lane of Class 70 R or
ii) Three lanes of class 'A" loading whichever, produces worst stress.
 Abutment

a) Due to class 70 R Wheeled

I) For Max Reaction on Abutment

Maximum Reaction occurs at end "A"

17 12
17 12
1370 3050 1370 2130 1520

400 10000 400

VB
VA = [ 17.0 10.40 9.03 5.98 4.61 12.00 2.48
x( + + + )+ x( +
= 0.96 10.0 = 55.16 T
)]/
VB = 92.0 - 55.16 = 36.84 T

Braking Force = 0.20 x 92.0 == 9.0

T

b) Due to class 70 R Tracked

I) For Max Reaction on Abutment
Minimum Reaction occurs at A

4570

-
400 10000 400
VA VB

VA = 1 / 10.0 x 70.0 7.72 = 54.01 T

x
VB = 1 x 70.0 - 54.01 16.00
= T
Braking Force = 0.20 x 70.0 = = 14.00 T

c) Due to class "A" ( Three lanes )

I) For Max Reaction on Abutment
Maximum Reaction occurs at end "A"

11.4 11.4 6.8 6.8

1200 4300 3000

400 10000 400

 Abutment

VA 17 17 VB
8 12 17 17
Vertical Reaction for three lanes of loading
VA = 3x [ 11.4 10.4 9.2 6.8 4.90 1.90 10.0
x( + )+ x( + )]/
= 80.9
T
VB = 109.2 - 80.9 28.30 36.4
= T
Braking Force = 0.20 x 36.4 = 7.3
T
Summary of L.L Rection and Braking force

Loading class Maximum Reaction Minimum Reaction Braking Force (Tonne) Case
(Tonne) (Tonne)

Class 70R (wheeled) 55.16 36.8 9.0 I

- single lane
Class 70R (Tracked) 54.01 16.0 14.00 II
- single lane
Class A (three lanes) 80.90 36.4 7.3 III
Class 70R (wheeled)
-1 lane + class A 1 82.13 49.0 16.3 IV
lane
Class 70R (tracked)
-1 lane + class A 1 80.97 28.1 21.28 V
lane
From above it can be seen that case (IV) will be critical
As per cl. 211.5.1.1 of IRC 6 - 2017 friction coef .for concrete over concrete surface
m = 0.50
Frictional force due to dead load + maximum live load reaction
,= 0.50 x( 150.0 + 82.13 )
= 116.1 T
Moment at R.L 472.55 m =( 476.8 - 472.55 116.1
)x
= 496.8 Tm
473.15 m =( 476.8 - 473.15 116.1
)x
= 427.1 Tm
As per cl. 211.5.1.2 of IRC 6-2017 maximum of m.Rg or Fh is to be considered. Hence ignore
other horizontal force on superstructure including seismic force.

Earth Pressure
Coeff of active earth press. KA = Cos 2 30.0
30.0 20.1 30.0 20.1 2
1 + sqrt[ {sin ( + )x sin ]
= 0.279

} / cos
Coeff of passive Earth press. KP = Cos 2 30.0
30.0 20.1 30.0 20.1 2
1 + sqrt [ {sin ( + ) x sin }/ cos
= 5.751
 Abutment

a) LWL case

1200
Deck Level =
477.74
RL
0.279 1.2 1.9 0.637
x x =

0.279 4.59 1.9 2.434

x x = 473.15
RL
0.279 0.60 1.9 0.318
x x =
472.55
RL

Earth Pressure and Moment @ RL 473.15 m

Sl Item Earth Pressure (Tonnes) L.A (M) Moment (T-M)
0.637 4.586 12.000
x `x
1 From RL 477.740 = 35.05 2.94 102.87
RL
To RL 473.154 2.43 4.59 12.000
1/2 x x x
= 66.97 1.93 129.00
Total = 102.02 231.87

Earth Pressure and Moment @ RL 472.55 m

Sl Item Earth Pressure (Tonnes) L.A (M) Moment (T-M)
From RL 477.740 231.87
RL
1 To RL 473.154 102.02 0.60 61.21
2.43 0.600 12.300
x x
From RL 473.154 = 17.96 0.38 6.90
RL
2 To RL 472.554 0.32 0.600 12.300
1/2 x x x= 1.18 0.25 0.30
Total = 121.16 300.28
 Abutment

b) HFL case

1200
Deck Level =
477.74
RL
0.279 1.2 1.9 0.637
x x =

0.279 2.16 1.9 1.146

x x = 475.58 HFL

0.279 2.43 1.0 0.678

x x = 473.15
0.279 0.60 1.0 0.168 RL
x x = 472.55
RL

Earth Pressure and Moment @ RL 473.15 m

Sl Item Earth Pressure (Tonnes) L.A (M) Moment (T-M)
0.637 2.16 12.00
1 From RL 477.740 x x= 16.51 3.81 62.87
RL
To RL 475.580 1.15 2.16 12.00
1/2 x x x= 14.86 3.33 49.52
1.783 2.43 12.00
2 From RL 475.580 x x= 51.92 1.21 62.97
RL
To RL 473.154 0.68 2.43 12.00
1/2 x x x= 9.86 0.80 7.90
Total = 93.15 183.26

Earth Pressure and Moment @ RL 472.55 m

Sl Item Earth Pressure (Tonnes) L.A (M) Moment (T-M)
From RL 477.740 183.26
RL
1 To RL 473.154 93.15 0.60 55.89
2.46 0.600 12.300
From RL 473.154 x x= 18.16 0.30 5.45
RL
2 To RL 472.554 0.17 0.600 12.300
1/2 x x x= 0.62 0.20 0.12
Total = 111.93 244.72
 Abutment

Loads and Forces on Foundation

The loads and forces on foundation and their moments about toe marked "X" are as follows
V H Lever Arm Moment
Sl Particulars of Dead Load
(T) (T) (m) (T-m)

1 Dead Load from superstructure 150.0 2.60 390.0

2 Dirt Wall = 12.00 0.20 0.91 5.4 2.90 15.8

x x x 2.5
3 Bearing Beam

12.000 0.60 0.50 2.50 9.0 2.70 24.3

4 Front Wall x x x
+ (b) ) x x 2.4
12.00 0.60 3.38 2.50 60.8 2.70 164.3
x x x
12.00 0.4 3.38 2.50 20.3 2.27 46.0
1/2x x x x
5 Return wall

2.40 0.35 4.59 2.50 19.3 4.50 86.7

2x x x x
2.40 0.35 4.59 2.50 9.6 4.00 38.5
2x1/2x x x x
6 Raft
x x x 2.4
5.40 12.30 0.40 2.50 66.4 2.70 179.3

2.00x 12.30 x 0.20 x 2.50 6.2 1.33 8.2

1/2x x x x
2.40 12.30 0.20 2.50 7.4 3.80 28.0
1/2x x x x
7 Earth on toe upto scour level

12.30 2.00 1.50 1.90 70.1 1.00 70.1

x x x
8 Earth behind front wall
11.83 2.40 4.69 1.90 252.7 4.20 1061.2
x x x
9 Earth on two side
x x x
0.15 3.40 4.69 1.90 4.5 4.20 19.1
2x x x x
10 Sub-Total without L.L 681.7 2131.5

11 L.L (max) 82.1 2.60 213.5

L.L (min) 28.1 2.60 73.1

12 Total with L.L (max) ( Normal case) 763.9 2345.1

Total with L.L (min) ( Normal case ) 709.9 2204.7

13 Total with L.L (max) ( Seismic case) 698.2 2174.2

Total with L.L (min) ( Seismic case ) 687.4 2204.7

 Abutment

Buoyancy force on foundation

(a) Under LWL condition

Volume = 5.40 12.30 2.15 142.54 M3
x x =
Upward force = -142.54 T

Weight of water in front

Downward load of water in front = 2.00 12.30 2.15

x x
= 52.79 T

Net upward force = -142.54 + 52.79 = -89.75 T

x
(b) Under HFL condition
Volume = 5.4 12.30 3.03
x x = 200.99 M3

Upward force = -200.99 T

Weight of water in front

x
Downward load of water in front = 2.00 12.30 3.03
x x
= 74.44 T

Net upward force = -200.99 + 74.44 = -126.55 T

x
Seismic force on foundation

Seismic coefficient = = 0.180

Seismic force and moments @ 472.55

RL H.F L.A
Sl Vertical load (T) Moment (T-m)
(T) (m)

1 Super structure D.L = 150.00 0.00 0.00 0.0

2 Dirt Wall = 5.44 0.98 4.73 4.63

3 Bearing Beam = 9.00 1.62 4.03 6.53

4 Front wall = 60.84 10.95 2.29 25.08

20.28 3.65 1.73 6.30

5 Return Wall 19.26 3.47 4.89 16.94

9.63 1.73 3.06 5.30

6 Earth on back of front wall

252.68 45.48 2.84 129.31

7 Earth on two side =

4.54 0.82 2.84 2.32

Total = 68.70 196.41

Vertical seismic force = 2 / 3 x 68.70 45.80 T

 Abutment

=
x =
Check for safety and stability of the Foundation

Area of the foundation A = 12.30 5.4 66.42 M2

x =
Section Modulus Z xx = 12.30 5.40 2 = 59.78 M3
x /6
Section Modulus Z yy = 5.40 12.302 = 136.16 M3
x /6
For F.O.S against faiulure refer cl.706.3.4 of IRC 78 - 2014

A ) Seismic Condition

1) LWL Condition

a) L.L (max ) case - Seismic downward

I) Base pressure

Vertical Load "P" = 698.2 45.80 89.75 654.21 T

+ - =
Moment @ toe Mt = -2345.1 0.0 300.28 496.8 196.4
+ + + +
+ 0.0 0.00 -1351.63
- = T-m
Eccentricity "e" from c.g = -1351.63 654.21 2.70 0.63
/ + = m
Moment @ C.g = 654.21 0.63 414.73 T-m
x =
Base pressure = 654.21 66.42 +/- 414.73 59.78
/ /
= 9.85 +/- 6.94 /

Pmax = 16.79 T/m2 Pmin = 2.91 T/m2

30.0
< 1.25 x T/m2

ii) Sliding

Coefficient of friction between concrete against soil = Tan f

For f = 36 o Tan f = 0.73

Vertical Load "P" = 654.21 T

Restoring force = 0.73 654.21 0.00 474.99 T

x + =
Disturbing force = 116.07 121.16 68.70 0.00 305.93 T
+ + + = T T
F.O.S = 474.99 305.93 = 1.55 > 1.15 - (SAFE) -
/ m m

iii) Overturning

Stabilising Moment = 2345.1 0.00 2345.1 Tm

+ =
Disturbing Moment = 0.00 300.28 496.8 196.41 = 993.45 Tm
+ + + T T
F.O.S = 2345.1 993.45 = 2.36 > 1.50 - (SAFE) -
/ m m
 Abutment
T T
- -
/ m m

b) L.L (min ) case - Seismic upward

I) Base pressure

Vertical Load "P" = 687.35 45.80 89.75 = 551.81 T

- -
Moment @ toe Mt = -2204.7 0.00 300.3 496.8 196.4
+ + + +
+ 0.00 -1211.22
= T-m
Eccentricity "e" from c.g = -1211.22 551.81 + 2.70 = 0.505 m
/
Moment @ C.g = 551.81 x 0.505 = 278.66 T-m

Base pressure = 551.81 / 66.42 +/- 278.66 59.78

/ /
= 8.31 +/- 4.66 /

Pmax = 12.97 T/m2 Pmin = 3.65 T/m2

< 1.25 x 30.0 T/m2

ii) Sliding

Vertical Load "P" = 551.81 T

Restoring force = 0.73 551.81 + 0.00 400.64 T

x =
Disturbing force = 116.07 + 121.16 + 68.70 0.00 = 305.93 T
T T
-
- -
F.O.S = 400.64 / 305.93 = 1.31 > 1.25 m
(SAFE) m

iii) Overturning

Stabilising Moment = 2204.7 + 0.00 2204.67 Tm

=
Disturbing Moment = 0.00 + 300.28 + 496.8 + 196.41 = T 993.45 T
- -
F.O.S = 2204.7 / 993.45 = 2.22 > 1.5 m
(SAFE) m
2) HFL Condition

a) L.L (max ) case

I) Base pressure

Vertical Load "P" = 698.15 - 126.55 - 45.80 = 525.81 T

Moment @ toe Mt = -2345.1 + 0.0 + 244.7 + 496.8 + 196.41

- 0.00 = -1407.2 T-m

Eccentricity "e" from c.g = -1407.2 525.81 + 2.70 = 0.024 m

/
Moment @ C.g = 525.81 x 0.024 = 12.49 T-m

Base pressure = 525.81 / 66.42 +/- 12.49 59.78

/
/
= 7.92 +/- 0.21
 Abutment

Pmax = 8.13 T/m2 Pmin = 7.71 T/m2

< 1.25 x 30.0 T/m2

ii) Sliding

Vertical Load "P" = 525.81 T

Restoring force = 0.73 x 525.81 + 0.00 = 381.76 T

Disturbing force = 116.07 + 111.93 + 68.70 = 296.69 T T

-
F.O.S = 381.76 / 296.69 = 1.29 > 1.25 (SAFE) m

iii) Overturning

Stabilising Moment = 2345.1 + 0.00 = 2345.1 Tm

Disturbing Moment = 0.00 + 244.72 + 496.8 + 196.41 = 937.89 T

-
F.O.S = 2345.1 / 937.89 = 2.50 > 1.50 (SAFE) m

b) L.L (min ) case

I) Base pressure

Vertical Load "P" = 687.35 - 126.55 - 45.80 = 515.01 T

Moment @ toe Mt = -2204.7 + 0.0 + 244.72 + 496.8 + 196.41

- 0.00 = -1266.78 T-m

Eccentricity "e" from c.g = -1266.78 / 515.01 + 2.70 = 0.240 m

Moment @ C.g = 515.01 x 0.240 = 123.74 T-m

Base pressure = 515.01 / 66.42 / +/- 123.74 / 59.78

/
= 7.75 +/- 2.07

Pmax = 9.82 T/m2 Pmin = 5.68 T/m2

< 1.25 x 30.0

ii) Sliding

Vertical Load "P" = 515.01 T

Restoring force = 0.73 x 515.01 + 0.00 = 373.92 T

Disturbing force = 116.07 + 111.93 + 68.70 = 296.69 T T

-
F.O.S = 373.92 / 296.69 = 1.26 > 1.25 (SAFE) m

iii) Overturning
 Abutment

Stabilising Moment = 2204.7 + 0.00 = 2204.67 T-m

Disturbing Moment = 0.00 + 244.72 + 496.8 + 196.4 = 937.89 TT

--
F.O.S = 2204.7 / 937.89 = 2.35 > 1.50 (SAFE) mm

B ) Normal Condition

1) HFL Condition

a) L.L (max ) case

I) Base pressure

Vertical Load "P" = 698.15 - 45.80 = 652.35 T

Moment @ toe Mt = -2345.1 + 244.72 + 496.76 - 0.0 + 0.0 = -1603.6 T

-
+ = 0.242 m m
Eccentricity "e" from c.g = -1603.59 / 652.35 2.70

Moment @ C.g = 652.35 x 0.242 = 157.76 T-m

Base pressure = 652.35 / 66.42 +/- 157.76 / 59.78

/
= 9.82 +/- 2.64

Pmax = 12.46 T/m2 Pmin = 7.18 T/m2

< 30.0 T/m2 (SAFE)

ii) Sliding

Vertical Load "P" = 652.35 T

Restoring force = 0.73 x 652.35 + 0.0 = 473.6 T

Disturbing force = 111.93 + 116.07 = 227.99 T = TT

--
F.O.S = 473.64 / 227.99 = 2.08 > 1.50 (SAFE) mm

iii) Overturning

Stabilising Moment = 2345.1 + 0.0 = 2345.1 Tm

Disturbing Moment = 244.72 + 496.76 - 0.0 + 0.0 = 741.5 Tm TT

--
F.O.S = 2345.1 / 741.48 = 3.16 > 2.00 (SAFE) mm

b) L.L (min ) case

I) Base pressure

Vertical Load "P" = 687.35 - 45.80 = 641.55 T

Moment @ toe Mt = -2204.7 + 244.7 + 0.0 + 496.8 - 0.00 = -1463.2 T

-
+ = m m
Eccentricity "e" from c.g = -1463.19 / 641.55 2.70 0.419
 Abutment

x =
Moment @ C.g = 641.55 0.419 269.00 T-m
/
Base pressure = 641.55 66.42 / +/- 269.00 / 59.78
/
= 9.66 +/- 4.50
 Abutment

Pmax = 14.16 T/m2 Pmin = 5.16 T/m2

< 30.0 T/m2 (SAFE)

ii) Sliding

Vertical Load "P" = 641.55 T

x + =
Restoring force = 0.73 641.55 0.0 465.8 T
+ + = TT
Disturbing force = 111.93 116.07 0.00 227.99 T
--
/ mm
F.O.S = 465.80 227.99 = 2.04 > 1.50 (SAFE)

iii) Overturning
+ =
Stabilising Moment = 2204.7 0.0 2204.7 T
+ + = TT
Disturbing Moment = 244.72 0.00 496.8 741.48 --
/ mm
F.O.S = 2204.7 741.48 = 2.97 > 2.00 (SAFE)

2) LWL Condition

a) L.L (max ) case

I) Base pressure
=
Vertical Load "P" = 698.15 - 89.75 608.41 T
+ + + - = T
Moment @ toe Mt = -2345.1 0.00 300.3 496.8 0.00 -1548.04 -
+ = m m
Eccentricity "e" from c.g = -1548.04 / 608.41 2.70 0.156
x =
Moment @ C.g = 608.41 0.156 94.66 T-m
/ /
Base pressure = 608.41 66.42 +/- 94.66 59.78
/
= 9.16 +/- 1.58

Pmax = 10.74 T/m2 Pmin = 7.58 T/m2

T/m2
< 30.0 (SAFE)

ii) Sliding

Vertical Load "P" = 608.41 T

x + =
Restoring force = 0.73 608.41 0.0 441.74 T
+ + = TT
Disturbing force = 116.07 121.16 0.00 237.23 T --
/ mm
F.O.S = 441.74 237.23 = 1.86 > 1.50 (SAFE)

iii) Overturning
+ =
Stabilising Moment = 2345.1 0.0 2345.1 Tm
 Abutment

+ + = TT
Disturbing Moment = 0.00 300.28 496.8 797.04 --
/ mm
F.O.S = 2345.1 797.04 = 2.94 > 2.00 (SAFE)

b) L.L (min ) case

I) Base pressure
=
Vertical Load "P" = 687.35 -
89.75 597.61 T
+ + + - = T
Moment @ toe Mt = -2204.7 0.00 300.3 496.8 0.00 -1407.63 -
+ = m m
/
Eccentricity "e" from c.g = -1407.63 597.61 2.70 0.34
x =
Moment @ C.g = 597.61 0.3 205.91 T-m
/ /
Base pressure = 597.61 66.42 +/- 205.91 / 59.78

= 9.00 +/- 3.44

Pmax = 12.44 T/m2 Pmin = 5.55 T/m2

T/m2
< 30.0 (SAFE)

ii) Sliding

Vertical Load "P" = 597.61 T

x + =
Restoring force = 0.73 597.61 0.0 433.90 T
+ + = TT
Disturbing force = 116.07 121.16 0.00 237.23 T --
/ mm
F.O.S = 433.90 237.23 = 1.83 > 1.50 (SAFE)

iii) Overturning
+ =
Stabilising Moment = 2204.7 0.0 2204.7 Tm
+ + = TT
Disturbing Moment = 0.00 300.28 496.8 797.04 --
/ mm
F.O.S = 2204.7 797.04 = 2.77 > 2.00 (SAFE)

Design of Raft

500
Y
X1
X3 X2

o
5.71
X2 X1
X3
Y
1800
 Abutment

2400 1000 2000

Case I - Seismic downward - LWL-L.L (max)

X Y

2.91
T/m2 7.54 9.08 10.48 16.79
12.06 T/m2
X
Y

UPWARD SOIL PRESSURE

9.85

3.80

DOWNWARD SOIL PRESSURE

= x x - x
S.F at Y-Y 12.06 1.50 + 1/2 x 4.73 1.50 3.80 1.50
= 15.93 T 2
x x / 2 + 1/2 x x 0.67 x
B.M at Y-Y = 12.06 1.50 1.50 4.73 1.50
2
x =
- 3.80 1.50 2 12.85 Tm
2
x x / 2 + 1/2 x x 0.67 x
B.M at X1-X1 = 10.48 2.00 2.00 6.31 2.00
2
x / =
- 3.80 2.00 2 21.81 Tm
2
x x / 2 + 1/2 x x 0.33 x
B.M at X2-X2 = 2.91 2.40 2.40 6.17 2.40
2
x / =
- 9.85 2.40 2 -14.13 Tm
2
x x / 2 + 1/2 x x 0.33 x
B.M at X3-X3 = 2.91 1.80 1.80 4.63 1.80
2
x =
- 9.85 1.80 2 -8.77 Tm

Case II - Normal - LWL-L.L (max)

7.58
 Abutment

T/m2 8.63 8.98 9.30 10.74

9.66 T/m2

UPWARD SOIL PRESSURE

9.85

3.80

DOWNWARD SOIL PRESSURE

= x x - x
S.F at Y-Y 9.66 1.50 + 1/2 x 1.08 1.50 3.80 1.50
= 9.61 T
2
x x / 2 + 1/2 x x 0.67 x
B.M at X1-X1 = 9.66 1.50 1.50 1.08 1.50
2
x / =
- 3.80 1.50 2 7.41 Tm
2
x x / 2 + 1/2 x x 0.33 x
B.M at X2-X2 = 7.58 2.40 2.40 1.41 2.40
2
x / =
- 9.85 2.40 2 -5.22 Tm
2
x x / 2 + 1/2 x x 0.33 x
B.M at X3-X3 = 7.58 1.80 1.80 1.06 1.80
2
x / =
9.85 1.80 2x -3.12 Tm
+

Use M 35 grade concrete with Fe 500 rebar, permissible stresses as per

Table A4.2 and A4.4 of IRC 112 are
Kg/ cm2 Kg/ cm2
s c = 116.7 s t = 2400 m= 10
( x ) = 0.33
n= 10 116.7
( x + )
10 116.7 2400
/3=
j= 1 - 0.33 0.89
1/2 x x x
Q= 0.33 0.89 116.7 = 17.01

a) At section X1-X1
Seismic case will be critical
- =
Effective Depth = 60.0 10.0 50.0 cm
2
x x
M.R =1.5x 17.01 100 50.0 = 63.78 T-m > 21.81 T-m (OK)
 Abutment

x 10 5 / ( x x
As = 21.81 0.89 50.0 3600 ) = 13.60 cm2

Min steel @ 0.13 % = 6.50 cm2

Provide 20 dia @ 200 c/c at bottom

As provided = 15.70 cm2

Check for shear at Y-Y

- =
Effective Depth = 55.0 10.0 45.0 cm
S.F = 15.93 T B.M = 12.85 Tm
Refer cl. A4.6.1 (b) of IRC:112
Effective S.F = 15.93 - 12.85 x tan 5.71
0.45
= 13.08 T
x
)=
Nominal shear stress = 13.08 x 1000 / ( 100.0 50.0 2.62 Kg/cm2
% age of tension reinforcements = 15.70 / ( 100 x 50.0 ) x 100 = 0.31 %
From Table A4.6 of IRC 112, Permissible shear stress = 2.30 Kg/cm2
=
Under seismic case = 1.5 x 2.30 3.45 Kg/cm2

b) At section X2-X2
Seismic case will be critical
-
Effective Depth = 60.0 10.0 = 50.0 cm
2
M.R =1.5x 17.01 x 100 x 50.0 = 63.78 T-m > 14.13 T-m (OK)
x 10 / (5
As = 14.13 0.89 x 50.0 x 3600 ) = 8.81 cm2

Min steel @ 0.13 % = 7.60 cm2

Provide 16 dia @ 200 c/c at top

As provided = 10.05 cm2

Design of Abutment Shaft

Seismic force at the base of the shaft

Seismic coefficient = = 0.18

Seismic force and moments @ RL 473.15

Sl Vertical load (T) H.F L.A Moment (T-m)

(T) (m)

1 Super structure D.L = 150.0 0.00 0.00 0.0

2 Dirt Wall = 5.44 0.98 4.13 4.04

3 Bearing Beam = 9.00 1.62 3.43 5.56

4 Front wall = 60.84 10.95 1.69 18.51

 Abutment

20.28 3.65 1.13 4.11

5 Return Wall 19.26 3.47 4.29 14.86

9.63 1.73 2.46 4.26

6 Earth on back of front wall 252.68 45.48 2.24 102.02

Total = 67.88 153.36

=
Vertical seismic force = 2 / 3 x 67.88 45.26 T

Loads and Forces at the base

The loads and forces on shaft and their moments about toe are as follows
V H Lever Arm Moment
Sl Particulars of Dead Load
(T) (T) (m) (T-m)

1 Dead Load from superstructure 150.0 0.100 15.0

2 Dirt Wall = 5.4 0.400 2.2

3 Bearing Beam + )x x 2.4 9.0 0.200 1.8

4 Front Wall 60.8 0.200 12.2

x x 20.3 -0.232 -4.7

5 Sub-Total without L.L 245.6 26.4

6 L.L (max) 82.1 0.100 8.2

L.L (min) 28.1 0.100 2.8

7 Total with L.L (max) (Normal case ) 327.7 34.7

Total with L.L (min) (Normal case) 273.7 29.3

8 Total with L.L (max) (Seismic case ) 262.0 28.1

Total with L.L (min) (Seismic case) 273.7 29.3

Summary of Force and Moments @ at base of shaft

1) Normal case under LWL
I) Max L.L case
Sl. No Item Vertical H.F ( T ) Moment ( T-m )
Load (T)
Long Tran Long Tran
1 Vertical Load 327.7 0.00 0.00 0.00 0.00
2 Eccentricity of Load 0.00 0.00 0.00 -34.65 0.00
3 Earth Pressure 0.00 102.02 0.00 231.87 0.00
4 H.F at Bearing 0.0 116.1 0.00 427.12 0.00
Total = 327.7 218.1 0.0 624.3 0.0
 Abutment

ii) Min L.L case

Sl. No Item Vertical H.F ( T ) Moment ( T-m )
Load (T)
Long Tran Long Tran
1 Vertical Load 273.7 0.00 0.00 0.00 0.00
2 Eccentricity of Load 0.0 0.00 0.00 -29.25 0.00
3 Earth Pressure 0.0 102.02 0.00 231.87 0.00
4 H.F at Bearing 0.0 116.1 0.00 427.12 0.00
Total = 273.7 218.1 0.0 629.7 0.0

2)Seismic case Under LWL

I) Max L.L case
Sl. No Item Vertical H.F ( T ) Moment ( T-m )
Load (T)
Long Tran Long Tran
1 Vertical Load 262.0 116.07 0.00 427.12 0.00
2 Eccentricity of Load 0.0 0.00 0.00 -34.65 0.00
3 Earth Pressure 0.0 102.02 0.00 231.87 0.00
4 H.F at Bearing 0.0 116.1 0.00 427.12 0.00
Total = 262.0 334.2 0.0 1051.5 0.0

ii) Min L.L case

Sl. No Item Vertical H.F ( T ) Moment ( T-m )
Load (T)
Long Tran Long Tran
1 Vertical Load 273.7 116.07 0.00 427.12 0.00
2 Eccentricity of Load 0.0 0.00 0.00 -29.25 0.00
3 Earth Pressure 0.0 102.02 0.00 231.87 0.00
4 H.F at Bearing 0.0 116.1 0.00 427.12 0.00
Total = 273.7 334.2 0.0 1056.9 0.0

Abstract of Force and Moments at the base of the shaft

Sl No Item Vertical Load ( T ) H.F ( T ) Moment (T-m) Remarks
1 Normal Condition
I) L.L (Max) 327.7 218.09 624.34
ii) L.L (Min) 273.7 218.09 629.74
2 Seismic Condition
(Seismic upward)

I) L.L (Max) 262.0 334.15 1051.46

ii) L.L (Min) 273.7 334.15 1056.86

From, above Seismic - L.L (Min) case will be critical

 Abutment

Design of Shaft
1) Case -1 LWL-Seismic-Min L.L
Design Data
Overall depth of the section h = 100.0 Cm
d
Effective Cover d = 10.0 Cm
Overall width of the section b = 1200.0 Cm
Thrust N d = 273.7 T As
Moment M d = 1056.9 T-m h
Modular Ratio m = 10.0

As

Calculation
=
Eccentricity e = 1056.86 / 273.7 3.86 M
Effective depth d = 90 Cm
Follow method 3 ( of Table 140 of Reynold's Handbook)

Method - 3
(Applicable when e > 1.5 * h

Providing 80 Nos 25 dia on earth face and 80 Nos.16 dia on other face
Area of steel provided A st = 392.8 Cm2 A sc = 160.8 Cm2

Taking moment about N-A c

b x n x n/2 + (m-1)x Asc x (n-d' ) = m x Ast x (d - n ) c

n
or, 1200 xn / 2 + 9 x
2
160.8 x ( n - 10 ) = 10 x 392.8
x ( 90.0 - n)
Or, 600 n + 2
1447.2 n - 14472.0 - = 353520 + 3928 n
Or, n2 + 8.96 n - 613.32 = 0
Or, n = 20.69 cm
(d-n)

c = 0.52 c

Lever arm 90.0 20.69/ 3 = 83.10 cm

-
=
Equating external Moment with that of the internal moment at the c.g of tensile steel
1200.0 x 20.7xC/2 x 83.10 + 9 x 160.8 x 0.52 xCx ( 90.0 - 10.0 ) = 1056.86
 Abutment

Or, C = 96.8 Kg/cm2

 Abutment

From the stress diagram

t= 3244.5 Kg/cm2

Stress in concrete due to direct load

c= 273.7 x 1000 / [ 1200 x 20.69 + ( 10 - 1) x 392.8 ]
c= 9.7 Kg/cm2
Total stress
In concrete = 96.8 + 9.7 = 106.5 Kg/cm2 < 1.5 x 116 for M35 conc.
In Steel = 3244.5 - 10 x 9.7 = 3148.0 Kg/cm2 < 1.5 x 2400

Check for Shear

Horizontal force H = 334.15 T

Nominal shear stress t= 334.15 x 10 3 / ( 1200 x 90.0 )= 3.09 Kg/ cm2

)
% age of tension reinforcements = 392.8 / ( 1200 x 90.0 ) x=100 = 0.36 %
From Table A4.6 of IRC 112, Permissible shear stress = 4.05 Kg/cm2
(under seismic case)
Hence no shear reinforcements is required.

Dirt Wall
Earth Pressure

1200 Deck Level =

RL 477.74

0.279 x 1.2 x 1.90 = 0.637

0.279 x 0.91 x 1.90 = 0.481

RL 476.83

S.F at RL. 476.83 m = 1.00 x 0.637 x 0.91

+ 1/2 x 0.48 x 0.91 = 0.58 + 0.22
= 0.79 T
B.M at RL 476.83 m = 0.58 x 0.64 x 0.91 + 0.22 x 0.42 x 0.91
= 0.42 TM
Effective Depth at A = 20.0 - 5.8 = 14.2 cm
 Abutment

2
M.R = 17.01 x 100 x 14.2 = 3.43 T-m > 0.42 T-m (OK)

As = 0.42 x 10 5 / ( 0.89 x 14.2 x 2400 ) = 1.37 cm2

Min steel @ 0.2 % = 2.84 cm2

Dirt wall to act as reaction block in the eventuality og earth quake provide extra reiforcement in
vertical direction

Provide 16 dia @ 150 c/c in vertical direction in both face and 12 dia @ 200 c/c in horizontal
direction
 Abutment

2.54599999999999
 Abutment

600
3000

5.186
5400

474.70
474.55

400 824

476.334 473.154
3.18

SAFE
#REF! 5400
5400
 Abutment

0
0

4860

0.017444
Abutment

92

11200
10000
5700
 Abutment

-3000

-6000

36.4

0.017444
cos f = 0.866158 cos2 f = 0.75023
sin( f+)d)== 0.766881 cos d = 0.939155
sin f = 0.49977
sin f + d = 0
cos d = 0.939155 cos f = 0.866158
sin f = 0.49977 sin (f+)d)== 0.766881
 Abutment

0.69974612111964

`
 Abutment

sin f = 0

`
 Abutment

2 x 1/2 x

2 x 1/2 x
 Abutment

`
 Abutment

126.55

0.00
Abutment

4000 #REF!
 Abutment

1
1

SAFE

474.99

4000 12

T/m2
 Abutment

0.00

4000 #REF!
 Abutment

0.00

4000 #REF!
 Abutment

5400

1.9 1.9
 Abutment

15 50

20 66.7
25 83.3

30 100
35 116.7
Abutment

0.60
Abutment

2
 Abutment

16.67
50.00
150.00
Follow method 1
Follow method 2
Follow method 3
Follow method 3

58.055

3277.158

50.33

20.69

81.4664
150

10

d-n = 69.312
1091357
 Abutment

d-n = 69.312
 Abutment

n= 20.69
t/m = 9.683898 184.6154

`
Abutment
Abutment
Abutment
 Abutment

75.35642
 Abutment

+
 Abutment

RETURN WALL

1.20

b = 4.79

4.79

2.540 0.637
a = 2.40

Earth pressue at top of pile cap = 0.279 x 1.90 x 4.79 = 2.54 t/m2

Pressure due to surcharge on return = 0.637 t/m2

Ref : Formulas for stress and strain by "Raymond J. Roark & Warren C. Young".

a = 2.40 m b = 4.79 m
a / b = 2.40 / 4.79 = 0.51

Case 11d for earth fill @ page no. 400

b1 = 0.34 b2 = 0.21 g1 = 0.50
moment at base of abutment
0.34 x 2.54 x 4.79 2 x 4.79 /( 6 x 4.79 )= 3.30 t-m/m
moment at face of abutment
0.21 x 2.54 x 4.79 2 x 2.40 /( 6 x 2.40 )= 2.04 t-m/m
Case 11a for surcharge @ page no. 399
b1 = 0.65 b2 = 0.65 g1 = 0.90
moment at base of abutment
0.65 x 0.64 x 4.79 2 x 4.79 /( 6 x 4.79 )= 1.58 t-m/m
moment at face of abutment
0.65 x 0.64 x 4.79 2 x 2.40 /( 6 x 2.40 )= 1.58 t-m/m

Total moment at base of wall = 3.30 + 1.58 = 4.88 t-m/m

Total moment at face of wall = 2.04 + 1.58 = 3.62 t-m/m

Overall thickness of Return wall = 350 mm

Effective thickness = 350 - 85 = 265 mm
2
M.R = 17.01 x 100 x 26.5 = 11.94 T-m > 4.88 Tm

Reinforcement in vertical direction

At = 4.88 x 10 5 / ( 0.89 x 26.5 x 2400 ) = 8.61 cm2
Provide 16 dia @ 150 c/c in vertical direction on earth face
 Abutment

Reinforcement in horizontal direction

At = 3.62 x 10 5 / ( 0.89 x 24.5 x 2400 ) = 6.90 cm2
Provide 16 dia @ 200 c/c in horizontal direction on earth face

Shear stress
Maximum shear force = 0.50 x 2.540 x 4.79 + 0.90 x 0.637 x 4.79
= 8.82 T
Nominal Shear stress =

8.82 / ( 4.79 x 0.265 )= 6.96 t/m2 = 0.70 kg/cm2

OK
 Abutment

1.80936
Abutment