Annexure - III

DESIGN OF AQUEDUCT
1. Hydraulic particulars of canal at the location of the structure
S.No.
1
2
3
4
5
6
7
8
9
10
11
12
13

Description
Units
Discharge Required
Cumecs
Designed
Cumecs
Bed Width
m
Full supply depth
m
Free board
m
Bed fall
m
Velocity
m/sec
Value of 'n'
Side slopes (I/O)
Top width of banks (E/P)
m
Canal bed level
m
Full supply level
m
Top of bank
m
G.L / SBL
m

Particulars
3.454
3.685
3.750
1.250
0.600
1 in 5800
0.5898
0.0200
1.5:1/
2.0:1.0
1.2 / 3.0 2.5 / 5.75
71.790
73.040
73.640
68.150

71.760

2 Stream Particulars:
1. Catchment Area =
12.846 Sq. Km
2. Stream bed level at crossing =
68.150 m
Catchment Area =
12.846 Sq. Km
Dickens Formula
Q = CM3/4
where C =
16.700 for catchment areas from > 2.5 & < 75 Sq. Kms
=
113.316 cumecs
3. Maximum Flood Discharge & Vent Way for stream flow:
Existing size of vent
=
3 v
3.50
Existing area of vent way
=
47.25 m2
Now proposed as
2
vent
with SLRB for continuty
Trough level
Roof level
Floor level

4. Vent way for Canal

1.5 times velocity =

7.00
x 4.50
of inspectionpath.
=
71.790
=
71.450
=
67.050

Size of Trough =

m clear span for stream flow.

m
m ( C.B.L-trough thickness - sealing coat)
m Existing

0.885 m/sec

Area of Trough required = Q /V

Size of Trough

x 4.50

3.685
0.885

4.165 =
1.250

3.332

3.750

Assume the thichkness of trough

Thickness of sealing coat
Size of Haunch
Trough level
Bottom level of Trough

x
=
=
=
=
=

4.1653 m2

1.850 m
0.225
0.04
0.075
71.790
71.450

III - 1

m
m
x
m
m

0.225 m

5. Transitions ( canal flow )

Normal bed width of canal
Width of the trough
=

3.750 m
3.750 m

5 m length of Transition with warped wings on either side.

5. 1.0 Stream flow

At entry & Exit
Width of Stream flow
Transition width
Length with 1 in 3 flare

13.36

Design of Stream Waterway

1 2

3
13.360

13.36
22
12.96
13

67.250

=
=
=
say

22.0

m at the structure
m
m
m
7
4

6' 6

67.05

Provide

=
=

22.0

Stream flow
3 4
1

5 6' 6
Canal Flow

13

13

10.250
Floor depth at exit with BY-WIER formula Q = 1.05 L H
113.316 =
There fore

1.5

1.05 x 22.0 H
2/3
113.316
23.1

1.5

2.887 m

Section 8 - 8: (Just outside the transition at the exit end)

+

69.937
68.450

2.887
+

1.5:1
67.050

22 m
Maximum Flood discharge =
Maximum Flood Level at the end of transition =
Floor level =
Depth of flow available =
Area of flow =
(22.00 +
1.5 x
=
76.016 sq.m.
Velocity =
113.316 / 76.016
=
1.491 m/sec
V2/2g =
=

1.491 2 /
0.1133 m

69.937
69.937
70.050 m

MFL at 8 - 8 =
TEL at 8 - 8 =

113.316
69.937
67.050
2.887
2.887

cumecs
m
m
m
) x

2x

0.1133

III - 2

2.887

9.81 )

Section 7 - 7: (Just inside the transition at the exit end)

+

69.911

2.861
+

67.050

22
Assume a depth of flow of
Area

2.861 m
=
22
x
=
62.942 sq.m.
Wetted Perimeter
=
27.722 m
Velocity
V
=
113.316 / 62.942
=
1.800 m/sec
R hydraulic radius =
A/ P =
2.270 m
V2/2g
=
1.800 2 / (
=
0.1652 m
Loss of head =
0.5 x (
0.1652
=
0.0260
due to change in velocity from section 8 - 8 to section 7 - 7
TEL at 7 - 7 wrt section 8 - 8. =
70.050 +
=
70.076
TEL at section 7 - 7 wrt assumed depth =
=
67.0500 +
=
70.076
HENCE O.K.

2.861

2x

9.81 )
0.1133 )

0.0260

2.861 +

0.1652

Section 6 - 6: (Just outside the barrel at the exit end)

71.450
69.697
15

2.647
+

71.150

67.050
13.36 m

Assume a depth of flow of

Area
=

Velocity

=
=
=

Weted perimetre

Hydraulic mean depth R

V2/2g
=
=

2.647 m
13.36 m
+14.42
2
36.759 sq.m.
113.316/ 36.759
3.083 m/sec
13.360 + ( 2.00 x
18.758 m
= A/ P
=
3.083 2 /
(
0.4843 m

1.0198
1.9597

Loss of head due to gradual expansion =

=
0.3 x (
0.4843
=
0.0957
V2 n 2/ R 4/3 x L
frictional losses S =

S=

0.0019
2.7150

2.647

x 13.00 =

III - 3

x 2.647 )

m
2x

9.81 )

0.1652 )
V= Average velocity
R average
n Value
Length
0.0092

=
=
=
=

2.441 m/sec
2.115 m
0.018
13

(due to change in velocity from section 7 - 7 to section 6 - 6)

TEL at 6 - 6 wrt section 7 - 7. =
70.076 +
=
70.181

0.0957

TEL at section 6 - 6 wrt assumed depth =

=
67.0500 +
=
70.181
HENCE O.K.

2.647 +

0.4843

The barrel roof level is 71.450 which is more than M.F.L at section 6-6
Hence Barrel Runs partially
Section6' - 6' : (Just inside the barrel at the exit end)
71.450
71.15
+
69.697
15
2.647
+

+ 0.009

i.e

+ 69.697

67.050
-0.484
13.36 m

Area =

13.36
A=
=
=
=
=
=
3.083
=

Velocity
Wetted perimeter
R , A/P
V2/2g

+14.42
2.00
36.759
113.316
3.083
13.360 +
18.758
1.960
2
/
(
0.4843

TEL at 6 - 6 wrt section 6'- 6'. =

2.647

sq.m.
/ 36.759
m/sec
( 2.00 x
m

1.0198

2x

9.81 )

67.050 +
70.181

x 2.647 )

2.647

0.4843

Section 5 - 5: (Just inside the barrel at the location of pier under trough.)
71.45
71.15
+
69.646
15
2.596
+

67.050
0.000
12.36 m

Area =

Velocity
Wetted perimeter
R , A/P
V2/2g

TEL w.r.t assumed depth=

12.36
A=
=
=
=
=
=
3.389
=

+13.40
2.00
33.434
113.316
3.389
12.360 +
17.655
1.894
2
/
(
0.5855

69.646 +
=

2.596

sq.m.
/ 33.434
m/sec
( 2.00 x
m

1.0198

2x
m
0.585

70.231

III - 4

x 2.596 )

9.81 )

TEL at 5 - 5 wrt section 6- 6. =

=

70.181
70.231

+0.50

(0.5855

-0.484 )=

Section 4 - 4: (Just inside the barrel at the entrance end)

71.45
69.646
2.596
67.050
12.36 m
2.596 m
=
12.36

Assume a depth of flow of

Area A

+13.398

2.596

2
=
=
=

Velocity V
Wetted perimeter

=
V2/2g
=
=
Head loss due to change in velocity = 0.3 (
=
Friction Losses:
Average Area A

=
=
=

Avg.Wetted perimeter p
R

frictional losses

S =

S=

TEL @ 4 - 4

33.434
113.316
3.389
12.360 +
17.655
3.389
0.5855

sq.m.
33.434
m/sec
( 2.00 x
m
2
/
(
m
0.5855

2x
-

(33.43 +
33.434 sq.m
18 m

10 )
0.585 )

33.434 )/ 2

V= Average velocity
R average
n Value
Length

x 13.00 =

0.021

70.231 +
70.252

x 2.596 )

0.0000

= A/P
=
33.434
17.655
=
1.894 m
V2 n 2/ R 4/3 x L

0.0037
2.3430

1.0198

0.0207

0.021

Section 3 - 3: (Just outside the barrel at the entrance end)

69.880
2.830
67.050
13.36
Assume a depth of flow of

2.830 m
13.36

Velocity V

=
=

+ 14.492 x
2.00
39.411 sq.m.
113.316 / 39.411

III - 5

2.830

=
=
=
=

3.389 m/sec
1.894 m
0.018
13.000

=
=
=

V2/2g

2.875 m/sec
2.875 2 /
0.4214 m

(2 x

Loss of head due to sudden contraction =

=
0.3 x (
0.5855
=
0.0492
(Due to change in velocity from section 4 - 4 to section 3 - 3)
TEL at 3 - 3 wrt section 4 - 4. =
70.252 +
=
70.301
TEL at section 3 - 3 wrt assumed depth =
=
67.0500
+
=
70.301
HENCE O.K.

10 )

0.4214 )

0.0492

2.830

+0.4214

Section 2 - 2: Just inside the transition at the entry end:

70.225
3.175
67.050

0.000

22 m
Assume a depth of flow of
Area A

3.175 m
= (
22.000 x
=
69.841 sq.m.
wetted perimeter p
=
28.349 m
Velocity V
=
113.316 / 69.841
=
1.622 m/sec
V2/2g
=
1.622 2 /
(
=
0.1342 m
Loss of head due to gradual contraction =
=
0.2 x (
0.4214
=
0.0574
(Due to change in velocity from section 3 - 3 to section 2 - 2)
TEL at 2 - 2 wrt section 3 - 3 =
70.301 +
=
70.359
TEL at section 2 - 2 wrt assumed depth =
=
67.050
+
=
70.359
HENCE O.K.

3.175 )

2x

10 )

0.1342 )

0.0574

3.175

0.1342

Section 1 - 1: Just outside the transition at the entry end:

70.447
3.197

0.222

70.225

67.250

2.975
75 mm wearing coat
67.050
66.975

0.200

q =

5.151

113.316
=
5.151
22.000
q = 1.705 h3/2 + 0.8 (2gh)XH
=

1.705

Cumecs / running metre

h3/2

+0.8 (2g)

III - 6

h1/2 X

2.975

3.0210

1.705

h3/2

10.5

h3/2

6.182

h1/2

h=

0.22249026

Solving for h,
3.0210

3.0210

h1/2

( LHS =RHS )

MFL over the drop wall =

=

70.225
70.447 m

0.2225

6. Total Energy Levels in the Canal:

ENERGY LINES
(Line diagram)
4

1
3

2
U/S

D/S

Canal Waterway

AT FSL

3.75
7.50

71.790

71.790

7.50 AT FSL

17.000
5.000 m

5.000 m

4
2

Section : 4 - 4 (Just Outside the exit transition)

Cross Section
=
Side slopes
=
Area
Discharge of canal Q
Approach Velocity

=
=
=
=

Velocity Head @ section 4 - 4

=
=

3.750
x 1.250
1.5 :1

3.750
7.031
3.685
3.685
7.031
0.524
V2
2g
0.524
2x 9.81
0.014

CBL
FSL
T E L

=
=
=

71.790
73.040
FSL

T E L @ section 4 - 4

=
=

=
1.5 :1

1.250

+ 1.50
sq.m

x 1.250

m3/sec
m/s

2
m

3.750

73.040
73.054 m

III - 7

+
+

V2
2g
0.0140

x 1.250

Section : 3 - 3 (Just Inside the exit of waterway)

Cross Section
Area

=
=
=

Velocity

Velocity Head @ section 3 - 3

=
=

3.750
x 1.235
sq.m

3.750
4.633

x 1.235

1.235
3.750

=
=

3.685
4.633
0.795 m/s
V2
2g
0.795 2
2 x 9.81
0.032243 m

Loss of head due to gradual Expansion from section 4-4 to 3-3

=
0.200
x
0.0322 0.0140
=
0.0036
T E L @ section 3 - 3 (w.r. to previous section)
=
73.054
+
0.0036
=
73.058 m
T E L @ section 3 - 3 (w.r. to Assumed depth)
=
71.790
+ 1.235
+ 0.032
=
73.058 m
Hence, Assumed depth of the section is OK
Section :2 - 2(Just Inside the Entrance of Waterway)
Cross Section
Area

=
=
=

Velocity
3.750
side slopes = 0.0
Velocity Head @ section 3 -3

3.750
3.750
4.633

x 1.235
x 1.235
sq.m

1.235

=
=
=
=

3.685
4.633
0.795 m/s
V2
2g
0.795 2
9.810
0.032 m

Loss of head in the waterway portion from section2 - 2 to 3 - 3

Wetted Perimeter (P)

Hydraulic Radius (R)

=
=
=
=

b + 2* d
3.750
3.750
6.221

A
P
4.633
6.221

2
+

Mannings Roughness coefficient (n)

0.018

Surface fall (By Manning Equation)

Vn
R 2/3

0.7954
0.7448
0.00030

III - 8

x 1.235
2.4710

0.745

x 0.018 2
2/3

Length of waterway
=
Loss of head in the waterway portion from section 2 - 2 to 3- 3
=
=
TEL's @ section 2-2

=
=

3.750
1.500

x 1.258

+ 1.50
sq.m

Area

=
=

3.750
7.092

Velocity

3.685
7.092
0.520 m/s

=
=

Velocity Head @ section 1-1

=
1.258
=

0.0003 x 17.00
0.0052 m

73.058
73.060 m

Section : 1 - 1 (Just Outside the entry transition)

Cross Section
=
Side slopes
=

1.5 :1

17.000

0.0052

x 1.258

x 1.258

V2
2g
0.520
2
2 x 9.81
0.014 m

3.750
Loss of head due to gradual Contraction from section 3 - 3 to 4 - 4
=
0.100
=
0.002
T E L @ section 1 - 1 (w.r. to previous section)

T E L @ section 1 - 1 (w.r. to Assumed depth)

FSL. is at the
FSL arrived

+ 71.790

=
=

+ 1.25

q=
R=

2 1/ 3

( )
q
f

Maximum scour level

= 1.5 x R
= 4.862
=

70.447

=
=
=

f =

73.040
73.048 m
0.812 cm Hence ok

1.875 Average of coarse and fine sand

- 4.862

A cutt off of 2.0 m is provided at i.e @ 65.050 m on U/S

D/S
Mean scour depth =

q2
1. 34
f

1/ 3

( )

113.316

0.0138

0.002

113.316
= 5.151 cumecs
22.000
3.241 m

Max scour depth

q=

+ 73.060
+ 73.062 m

0.0322

=
+ 71.790
+ 1.258 + 0.014
=
+ 73.062 m
Hence, Assumed depth of the section is OK

Afflux

7. Scour Depth Calculations:

For stream
U/S
Mean scour depth =
1. 34

= 5.151 cumecs

III - 9

65.586 m

22.00

III - 10

R=

3.241 m

Max scour depth

Maximum scour level

= 1.5 x R
= 4.862
=

69.937

- 4.862

65.075 m

A cutt off of 2.0 m is provided at i.e @ 65.050 m on D/S

For Canal
U/S
Mean scour depth =

q=

q2
1. 34
f

1/ 3

( )

3.685
= 0.655 cumecs
5.625
0.820 m

R=
Max scour depth
Maximum scour level

= 1.5 x R
= 1.230
=

73.060

- 1.230

Avg length= ( bed width +width at fsl)/2

=
5.625 m

A cutt off wall of 1.50 m is provided at the u/s of Canal i.e

71.830 m
70.290 m

D/S
Mean scour depth =
q=
R=

1. 34

q2
f

1/ 3

( )

3.685
= 0.655 cumecs
5.63
0.820 m

Max scour depth

Maximum scour level

= 1.5 x R
= 1.230
=

73.040

1.230

A cutt off wall of 1.50 m is provided at the D/s of Canal i.e

III - 11

71.810 m
70.290 m

8. DESIGN OF TROUGH SLAB:

0.250
0.60

2.190

1.25

0.04
0.340
0.075

0.225
3.750

The following stresses are adopted

Stress in concrete ( c )

water side face

70 Kg/cm2

Stress in Steel
Concrete mix

=
=

1900 kg/cm2
M20 grade

Unit weight of R .C .C

2500 Kg/m2

Unit Weight of water

The other standard co-efficients are
m
n
j
Q

1000 Kg/m2

=
=
=
=

Away from water face

13.333
0.329
0.890
10.263

Size of trough
=
1
bay of
3.75
m width
depth of flow in the trough
=
1.250
m
Free board
=
0.60
m
Depth of water considered
=
depth of flow in the trough
+
free board
Depth of water considered
=
1.250
+
0.60
=
1.850 m
Depth of trough
=
1.850
m
width of bay
=
3.750
m
The trough bottom slab is designed as Simply supported spanning between beams
Assuming thickness of slab
=
225
mm with
40
mm thick sealing coat over it
Assuming clear cover of
30 mm and
Adopting
16
mm bars as main reinforcement
Effective depth of slab
=
225
30
8
=
187 mm or
18.7 cm
Effective span of slab

=
=
=

clear span

=
=

0.225
0.04

3.750
3.937

deff
0.187

Loads per metre length:

1) Self weight of slab
2) Weight of sealing coat

x
x

Total weight ( W)

III - 11

2500
2500

=
=

562.5
100

kg/m
kg/m

662.5

kg/m

10.1 DESIGN OF SIDE WALL OF TROUGH:

0.250
0.6
3.750

Mix adopted

Stress in steel

Q
J
n

=
=
=

1.25
2.190

M20
1900 Kg/cm2
10.263
0.890
0.329

C =
m =

70 Kg/cm2
13.333

0.04
0.225
0.075
0.225
Total height of side wall =
0.60
+
1.25
+
0.04
+
0.225
+
=
2.190
m (or)
219 cm
The side wall is designed as a simply supported beam in between the abutment & piers with
clear span of
7.00
m
to support the vertical load due to own weight and
the load coming from the trough slab and the water in the trough. The side wall is also checked for the water thrust
Assuming the width of beam
=
25 cm
Clear span
=
7.000 m
Top width of abutment
=
0.900 m
Width of pier
=
1.000 m
Width of bearing
=
0.494 m
Clear cover to beam
=
0.050
assume the dia of Main reinforcement =
20 mm
Effective depth of beam =
2190
50.0
10
=
2130.0 mm
=
213.0 cm
Effective span
=
7.000
+
0.494
=
7.494 m
Slenderness limits for beams to ensure lateral stability :
To ensure lateral stability, The clear distance between the lateral supports
according to para 23.3 of IS:456-2000 should not exceed.
i)
60b (or)
whichever is less
ii)
250 b2/d

0.075

Where
'd' is the effective depth of the beam and
'b' the breadth of the compression face
The clear distance between lateral supports
=
clear span
i)
ii)

60b
250 b2 / d
Mininum of above i and ii

=
=
=

=
=
x

60
250
733.57 cm
HENCE SAFE

7.00 m
700 cm
25
=
2.93
greater than

1500

cm

733.6
700

cm
cm

Check for vertical deflection:

As per para 23.2.1 of IS 456 : 2000 the vertical deflection limits may generally be assumed to be satisfied provided that
the span to depth ratio is less than
20
for Simply supported spans up to 10 m
20x 10/span for Simply supported spans greater than 10 m
Span
Eff. depth

=
=

i)
ii)
ii)
v)
v)
i)

LOADS (per m run) :

Dead load of side wall
Weight of trough slab
Wt. of sealing coat
weight of haunches
weight of fillets
weight of water

=
=
=
=
=
=

2.190
0.225
0.04
0.075
0.075
1.85

x
x
x
x
x
x

Bending moment BM = wl2 / 8

=
=

700.00
213.00
3.29

<

0.25
3.75
3.75
0.225
0.225
3.75

d (available)

x
x
x
x
x
x

/2
/2
/2
/2
/2

6121.88
x
4297559 Kgcm

MR
=
Q bd2
d(req.) = M/Qb
=
4297559
=
129.42 cm
213.000 cm
HENCE SAFE

Design same as done for Super Passage

III - 12

20
HENCE SAFE

2500
2500
2500
2500
2500
1000

=
=
=
=
=
=
Total weight:

7.494 2 x

100

10.26329

> d(Req.)

129.42 cm

25

1368.75
1054.69
187.50
21.09
21.09
3468.75
6121.88
/

Kg
Kg
Kg
Kg
Kg
Kg
Kg

9. Design of Canal aquaduct

Abutment
TBL

73.640

W8

1.85

w1 w1'

+71.790

W7

71.72

0.340
+71.150

+71.450
0.494

W6
P1

w2

W9

1
W3

5.100

5.740

0.494

P2

W5

5
0.250

W4

0.60

0.820

0.3

3.420
w5'
1.000
W 10

1.600
B

67.05 SBL
w4'
1.000
1.820
+66.050

1.250
2.190
0.04

0.500
+65.550

0.225
3.750

4.420
5.020

0.340

0.250
Density of concrete RCC
Density of concrete CC
Density of soil
Density of water
Surcharge Load
Width of bearing
Load from Trough

=
=
=
=
=
=
W1

=
=
=
=

From side walls (2 nos)

Trough slab
Sealing coat
haunches (2 nos)
Fillets (2nos)
Weight of water

2.0 x

2.0 x
2.00 x

=
=

2.500
2.400
2.100
1.000
1.100
0.494

0.25
3.75
3.75
0.225
0.150
3.75

x
x
x
x
x
x

t/m3
t/m3
t/m3
t/m3
t/m3

Clear span

2.190
0.225
0.04
0.075
0.15
1.85

x
x
x
x
x
x

7.988
7.988
7.988
7.988
7.988
7.988

7.00 m

x
x
x
x
x
x

2.50
2.50
2.40
2.400
2.400
1.000

Total Load
Load shared on abutment
Length of abutment

load / m run

=
=
=
=
=

W1

Load of w1'

49.259
1.00 x

t
3.75

4.750 m
49.259
10.370 t/m
0.506

+ 2 x
+ 2 x

4.750

0.3

0.250
0.250

=
=
=
=
=
=

21.867
16.850
2.876
0.647
0.863
55.417

98.519 t

( top width of side walls)

x 2.40 =

0.3643 t/m

Total Moments about 'A' at the base level

Load

Description

W 1+w1'

As calculated above w1+ w1'

Load (t)
Hor.

Ver.

L.A

Moment (t-m)

10.735

2.353

W2

0.494 x

0.640 x

2.400

0.759

1.847

1.401

W3

1.000 x

4.100 x

2.400

9.840

2.100

20.664

25.259

W4

0.500 x

0.820 x

4.100 x

2.400

4.034

2.873

11.592

W5

0.500 x

1.600 x

4.665 x

2.400

8.957

1.067

9.554

W6

0.500 x

1.600 x

4.215 x

2.100

7.081

0.533

3.777

0.525 x

2.400

2.016

0.800

1.613

1.850 x

1.000

3.874

1.047

4.056

1.757

----

W7

1.600 x

W8

2.094 x

Pv

0.0384 x

7.042^2 -2.83 ^2

1.100

Ph

0.1340 x

7.042^2 -2.83 ^2

1.100

6.132

2.390

14.655

1.000

8.769

2.37

20.783

P1

1.850 x

4.740 x

III - 13

t
t
t
t
t
t

P2

0.50 x

4.740 x

4.740 x

1.000
V

11.234
=

III - 14

49.053 t

1.580
M =

17.749
131.103 t - m

1.85
1.100

x 1.00

1.85
1.100

x 1.00 +

0.525 x

2.400

+4.215

2.400

7.042

1.100
0.525 x

2.827

1.100

Lever arm

=
=
=

M
131.103
2.673 m

Base Width (b)

1.710 m

Ecentricity

V
49.053

=
Lever arm - base width /2
=
0.963 m
=
b/6
=
0.570 m
<
0.963 m
Revise the section

Allowable ecentricity

Max. Compressive Stress

=
=

V/b (1 + 6 x e / b)
38.567 t / m2

Min.Compressive stress

=
=

V/b (1 - 6 x e / b)
-9.881 t / m2

Total Moments about 'B' at the base level

Description

W 1+w1'

As calculated above w1+ w1'

Ver.

L.A

Moment (t-m)

10.735

2.353

0.494 x

0.640 x

2.400

0.759

1.847

1.401

W3

1.000 x

4.100 x

2.400

9.840

2.100

20.664

0.500 x
0.500 x

0.820 x
1.000 x

4.100 x
1.000 x

2.400
2.400

4.034
1.200

2.873
3.753

11.592
4.504

0.500 x

1.600 x
3.420 x

4.625 x
1.000 x

2.400
2.400

8.880
8.208

1.067
1.710

9.472
14.036

0.500 x

1.600 x

5.215 x

2.100

8.761

0.053

0.467

0.525 x

2.400

2.016

0.800

1.613

1.850 x

1.000

3.874

1.047

4.056

2.100

----

W4

W5'
W6
W7

1.600 x

W8

2.094 x

25.259

Pv

0.0384 x

7.374^2 -2.16 ^2

1.100

Ph

0.1340 x

7.374^2 -2.16 ^2

1.100

7.328

2.818

20.651

P1
P2

Hor.

W2

W4'
W5

Load (t)

Load

0.50 x

1.850 x

5.740 x

1.000

10.619

2.870

30.477

5.740 x

5.740 x

1.000

16.474
V =

1.913
M =

31.520
175.711 t - m

converting water and concrete area in terms of soil

1.85
x 1.00
+
0.525 x
1.100
1.100
1.85
1.100

x 1.00 +

0.525 x

1.000

+5.215

1.000

1.100

Lever arm

=
=
=

M
175.711
2.909 m

Base Width (b)

2.210 m

V
60.407

III - 15

60.407 t

2.159

7.374

Ecentricity

=
Lever arm - base width /2
=
0.699 m
=
b/6
=
0.737 m
>
0.699 m
Hence Ok

Allowable ecentricity

Max. Compressive Stress

=
=

V/b (1 + 6 x e / b)
26.631 t / m2

Min.Compressive stress

=
=

V/b (1 - 6 x e / b)
0.703 t / m2

Total Moments about 'C' at the foundation level

Load

Description

W 1+w1'

As calculated above w1+w1'

W2
W3
W4
W4'
W5
W5'
W6

Moment (t-m)

10.735

2.653

28.479

0.494 x

0.640 x

2.400

0.759

2.147

1.629

1.000 x

4.100 x

2.400

9.840

2.400

23.616

0.820 x
1.000 x

4.100 x
1.000 x

2.400
2.400

4.034
1.200

3.173
4.053

12.802
4.864

0.500 x

1.600 x
3.420 x

4.100 x
1.000 x

2.400
2.400

7.872
8.208

1.367
2.010

10.758
16.498

0.500 x

1.600 x

5.215 x

2.100

8.761

0.353

3.096

0.525 x

2.400

2.016

1.100

2.218

1.600 x

W8

2.094 x

1.850 x

1.000

3.8739

1.347

5.218

W9

0.300 x
0.300 x

5.740 x
1.850 x

1.100
1.000

1.894
0.555

0.150
0.150

0.284
0.083
15.120

W 10

5.020 x

Pv

0.0384 x

Ph

0.1340 x

P1
P2

L.A

0.500 x
0.500 x

W7

Load (t)
Ver.

Hor.

0.50 x

2.400

6.024

2.510

7.899^2 -2.16 ^2

0.500 x

1.100

2.439

----

7.899^2 -2.16 ^2

1.100

8.510

3.029

25.777

1.850 x

6.240 x

1.000

11.544

3.12

36.017

6.240 x

6.240 x

1.000

19.469
V =

converting water and concrete area in terms of soil

1.85
x 1.00
+
0.525 x
1.100
1.100
1.85
1.100

x 1.00 +

0.525 x

=
=
=

M
226.955
3.327 m

Base Width (b)

2.510 m

Ecentricity
Allowable ecentricity

1.000

+5.740

1.000

1.100

Lever arm

V
68.211 t

=
Lever arm - base width /2
=
0.817 m
=
b/6
=
0.837 m
>
0.817 m
Hence Ok

Max. Compressive Stress

=
=

V/b (1 + 6 x e / b)
26.860 t / m2

Min.Compressive stress

=
=

V/b (1 - 6 x e / b)
0.315 t / m2

III - 16

68.211 t

2.080
M =
=

2.159

40.495
226.955 t - m
7.899

Design of Bed Blocks under trough:

1.

Weight of trough including Side walls, wearing coat, honches and Fillets

2.

Weight of water in the trough

=
55.42 t
Total Load = 98.52 t

Load on the Abutment

Load transmitted by each side beam

=
=

98.519
49.259

=
=

49.26
24.630

Therefore, Total Load on bed Block

=
24.630
t
= (0.494+0.012 ) x( 0.3+2*0.2 ) x 0.3
Providing a bed block of 0.506 m x 0.700 m x 0.3 m
Weight of bed block

=
=

0.506 x
0.266

Total load on the abutment under the bed block

Intensity of pressure under the bed block

43.102 t

=
=
=

=
=

24.90
0.506 x 0.7
70.286
t/m2
7.03
Kg /cm2

0.70

size
x

0.3

2.5

t
24.630
24.895 t

0.266

0.494
0.506
0.30

Which is Permissible.
Adopting the bed blocks in VRCC M 20
1.00
10 No.s 16 mm Bars
Providing 1% of G.S.A.
=
1 x
30 x
100
=
15
Sq. cm
No. of

16
Provide

Provide 4 Legged

mm diameter bars
5

bars at top &

mm bars

50.60

7.55

bars at bottom

10

No.s
Section X-X

300 c/c as transverse reinforce ment

III - 17

0.02
W7

TBL

73.565

73.640
W1

w3

72.975
W2
00

7.590

W6

0.49 72.675
71.15

W5

5.925

stresses at Base

max
31.134

min
3.648

67.050
1.000

stresses on soil

max
22.438

min
9.510

W8
W4

A 1.70
0.300
0.5

1.0

w5'
B

4.520

w4'
0.82
1.820 w4''
0.3

w9

66.050
65.550

5.120
Design same as done for Single Lane Road Bridge

III - 17

11.DESIGN OF PIER
+ 71.790
0.040
0.225
0.075

+ 71.450
71.150
1.000
SMFL

+ 69.646

4.900

0.5
0.5
0.5

0.3
0.3

1.000
1.600

0.3
0.3

SBL + 67.050
+ 66.550
+ 66.050
+ 65.550

2.200

5.550

4.550

1.000

6.150

1.600
2.200
Design same as done for Super Passage

III - 18

6.750

stresses at Base

max
33.984

stresses on soil

max
14.132

11.DESIGN OF PIER

min
23.047
min
9.495

III - 19

12 DESIGN OF PIER FOR SLRB

12.1.0 Details of structures
a. Carraiage way

4.25

b.Width of slab including kerbs o/o

5.0

c. Dia of column (assumed) circular

1.3

d. Dia of column at bottom

1.3

e.Size of footing

4.8

f. Depth of footing

0.60

g. Clear span in between bearing pedestal

7.0

h. Bearing

0.49

h.Effective span

7.49

i.Depth of hammer head

0.70

i. Effective cover

50

mm

Sectional properties of circular column and foundation

Diameter (D)

1.3

Percetage of steel assumed (Pt)

0.8

modular ratio

10

Area of column (Ac)

1.327

m2

Area of steel assumed

0.0106

m2

or

106.19

Equivalent area of concrete (Ae)

= Ac + (m-1) As
(10-1)

0.011

Moment of inertia I

(According to IRC 21 clause 303.1 )

1.327

1.423

m2

22

x D4

64

22

0.1403

1.3

7
Mean diametre of the column, Dm

Equivalent moment of inertia, Ie

cm2

64
m4

= D- 2 ('effective cover )
=

1.3

1.2

x0.05

x 0.0106

x1.20

= I +(m-1) As x D m 2 / 8
=

0.1403

+(10-1)

2
8

0.140

Equivalent moment of inertia, Ie

0.157

m4

Equivalent section modulus, Ze

Ie /d/2

0.157

0.242

m3

0.0172

1.30/2

Properties of column @ base

Equivalent area

1.423

m2

Z of column at base

0.242

m3

Radius og Gyration

radius

4.8

2
Properties of foundation section
Area

2
=

3.142

4
=

18.098

Zxx

3.142

4.8

32
=
Zyy

10.859
10.859

m3
m3

III - 19

0.727

RCL
Deck slab

0.075
0.590

+ 73.640
+ 72.975

72.175

1.000
2.529
1.3

6.025

SMFL

+ 69.646
2.596

SBL
1.300

+ 67.050
0.90
+ 66.150

1.500

0.30
+65.850
4.800

0.30
+65.550
+65.250

0.3
5.400

5.00
12.2.0 Loads comming on the columns
a) Dead load

0.25

1)Dead load from super structure.

2) Dead load from hammer head
3) Dead load from bearing pedestal

=
=
=

4) Weight of column
a. Up to footing

(72.175

- 66.150 )=

6.025

5. weight of column with 15 % buoyancy

73.561 t
8.669 t
1.25 t

1.3
(5x0.25+((5-1.30)/2)x0.45+1.3x0.45)x1.3x 2.5
(5.0x 0.1x2.5x1)

1.327

6.025 x

2.5

19.993 t
19.993

19.993

x 1.00
2.5

18.793 t

Volume of footing

10.334

Weight

25.834

x15.00
100

6. Weight of foundation

7. wieght of footing with 100 % buoyancy

(3.142x 4.8x4.8)/4x 0.3+(((3.142x4.8x4.8)/4)-((4.8-1.3)/2)x 0.3

25.834

1.5
2.5

15.501 t

b)Live load reaction

IRC class A loading
2.7
2.5

2.7
1.1

11.4
3.2

7.49
C

1.2
m

0.69

Reaction calculations
Taking moments about C
Ra x
7.49 =

12.549

7.49 =

11.400

Rb

14.469

Ra +Rb

27.017

6.8
4.3

0.51

6.80

6.8
3

0.19

7.49 m

Ra

11.4

Ra

11.4

Rb

2.700

x 3.60

+2.70

2.5

x3.19

+6.80

0.19

Taking moments about D

Rb x

7.490

6.8

and

Ra - Rb

III - 20

1.920 t

0.45

live load on bridge

27.017

Impact factor

4.5

t
=

0.33

( no impact as the height of the column is more than 3.0 m )

6+L
Live load reaction

27.017 t

Maximum reaction
Dead loads =

73.561 t

Dead load +Live load =

100.578 t

12. 3.0 Horizontal forces

7.3.1 Braking force or tractive force on column due to Class A train of vehicles
for span BD
Braking effect on simply supported span
Braking force

0.2 x ( 2 x 11.4 + 2 x 6.8 )

7.28 t acting at a height of

change in vertical reaction due to

Braking force

7.28

1.813 t

1.2

7.28

1.08

m above the Deck

x ( 1.2

+0.59

+0.075

)/

7.49

for span CA
Braking effect on simply supported span
Braking force

Braking force

1.08

0.269 t

Change in vertical reaction = Ra-Rb=

Moment at base of column
-

1.08 t acting at a height of

change in vertical reaction due to

( 72.975

0.2 x ( 2 x 7)
1.2

1.813 -

+ 66.150

m above the Deck

x ( 1.2

+0.59
0.269 =

7.28

1.080

66.150 )

+0.075

)/

7.49

1.544 t

6.825

2
=

moment about the top of the soil

+65.550 =

28.5285 tm
7.28

6.825

1.08 x(

+0.60 )

2
=

31.0365 t -m

12.3.2 Moment due to live load eccentricity

a)Eccentricity perpendicular to road way i.e in the stream flow direction (Longitudinal )
Distance of C.G of LL from the edge of the bridge (0.15+0.25+1.8/2 )
Eccentricity of loads from the centre line of bridge

4.25

-1.30

1.3 m

0.825 m

2
4.25
1.3

1.8

0.15 0.5

0.825

0.5

e
2.125
Max. live load reaction =

27.017 +

1.544 =

28.561 t

Considered at the point of action of live load i.e centre of bearing

Moment

28.561 x

0.825 =

b) Transverse eccentricity

23.563 t-m

0.02

0.51
1

0.245 m

1.3
Maximum live load Ra-Rb

Eccentricity

1.920 +

1.544 =

0.51

3.464 t
0.255 m

2
Moment

3.464 x

0.255 =
III - 21

0.883 t-m

12.4.0 Wind force (clause 212.3 of IRC -6:2000)

case A wind force on deck slab, column,column head and live load
Exposed height of

deck

0.665 m

Kerb

0.225 m

0.6 m

parapet of 0.6 height

1.490 m
C.G of exposed area
=

0.890 x

0.890

/2 +

0.6

x 1.190

0.890 +

0.6

+ 72.975 +

0.745 =

73.720 m

Height above stream flood level

73.720 -

+69.646 =

4.074 m

Height above SBL

73.720 -

+67.050 =

6.670 m

=
acting @ E.L

0.745 m

Horizontal wind pressure for

m height

40 Kg /m2

m height

52 Kg /m2

m height

63 Kg /m2

m height

73 Kg /m2

m height

82 Kg /m2

10

m height

91 Kg /m2

Horizontal pressure @

6.670 m height

76.015 Kg /m2

Horizontal pressure @

4.074 m height

63.370 Kg /m2

wind force at

4.074 m height

7.98

=
wind force at

6.670 m height

63.370 /

1000

1.490

76.015 /

1000

1.490

0.7535 t

7.98

0.9038 t

For sreamfull condition

Moment @ top of column base

0.7535 x

7.570 =

5.704 t-m

Moment @ top of soil

0.7535 x

8.170 =

6.156 t-m

Moment @ top of column base

0.904 x

7.570 =

6.842 t-m

Moment @ top of soil

0.904 x

8.170 =

7.384 t-m

For stream Empty condition

Case B Wind force on live load

case 1 Taking maximum length of vehicle permitted in one span , joint to joint =

7.98 m

As per clause 212.4 of IRC -6:2000 the wind force should be 300 kg/linear m for ordinary bridge .
For classA- loading,the max . force will be acing on
Wind force =

7.98 m length of truck with

7.98 x

300

Moment at the base of the column

Moment at the top of the soil

1000

2.394 t
acting at a height of

Total lever arm from the top of column

300 kg/m run

0.665
=

2.394

21.52 t-m

2.394

22.96 t-m

1.5 m above the road level

1.5

2.165

x(

2.165 +

6.825 )

x(

2.165 +

7.425 )

Case A+B total moment due to wind force on super structure and on Live load
Moment at the base of the column

6.8420

21.52 =

28.364 t-m

Moment at the top of the soil

7.384

22.96 =

30.343 t-m

Case 2 As per 212.6 of IRC -6 :2000 the wind force shall not be less than
450 kg/m acting @ kerb level i.e +
Height up to column base

73.865

73.865
-

+ 66.150 =
III - 22

7.715

Height above footing

73.865

7.98

Wind force =

+65.550 =
450

8.315
/

1000

3.591 t

Moment at the base of the column

3.591 x

7.715 =

27.70 t-m

Moment at the top of the soil

3.591 x

8.315 =

29.86 t-m

Case 3 As per 212.7 of IRC -6 :2000 the wind force shall not be less than
Wind force =

1.490

2.854 t

Moment at the base of the column

2.854 x

Moment at the top of the soil

2.854 x

Govering wind moments @ base of pier

28.364 t-m

Moment at top of the soil

30.343 t-m

240 kg/m2 is considered

240

7.98 /

7.570 =

1000

21.60 t-m

(6.67+0.9 )
8.170 =

23.31 t-m

12.5.0 Force due to water currents in the canal ( as per para 213.2.0 of IRC -6:2000)
Intencity of pressure due to water currents

P =

where k =
Maximum mean velocity of the canal(v)

52 K V2
0.66 (semi circular)

113.32 /

33.434 =

3.389 m/sec

Maximum velocity (V)= 2 v

1.414 x

3.389 =

4.792 m/sec

Maximum V2

Maximum velocity (U2) at base of column

22.966 m/sec
0

m/sec

V2 = 2 v 2 =

22.966

+ 69.646
4.1

+ 67.050

0 0

1.5
12.6.1 Water force across the direction of streamflow
Pressure @ MFL @ + (

case 1

transverse

+65.550

+ 69.646 )= 52 k v 2 sin 200

Intensity of pressure at MFL

Pressure @ SBL

52

269.583 kg/m

+ 67.050 =

Lever arm

0.66

22.966

sin 200

kg/m
2.596

x 2.00 =

1.731

3
Total force on the column

269.583

2.596

1.300

454.894 kgs

(1.731

0.90 )

1.197 t-m

2.631

0.6

)=

2
Moment at the base of the column

454.894

x
1000

Moment about the top of the soil

454.894

1.470

1000

12.6.2 force due to water currents along the direction of stream flow as per para 213.2.0 of IRC
Pressure @ MFL @

Pressure @ SBL @
Lever arm

=
=

52

740.672 kg/m

+ 0.000 =
=

(Case 2 )

52 k v 2 cos200

0.66

kg/m
1.731

m
III - 23

22.966

cos 200

t-m

Total force on the column

740.672

2.596

1.300

1249.8

kgs

0.90 ) =

3.288

t-m

)=

4.038

t-m

2
Moment at the base of the column

1249.812

(1.731 +

1000
Moment about the top of the soil

1249.812

x(

2.631 +

0.6

1000
The moment obtained in case (1) should not be less than the moments due to net hydrostatic pressure with a difference of
250 mm in water levels on opposite faces of column ( As per 213.6 of IRC bridge code ) as below

In Canal flow direction:

Water force in road way direction due to 250mm difference in water levels between the opposite
faces of the column

From clause 213.6 of IRC: 6-2000

250 mm

MFL + 69.646
2.596

1.3

69.396
2.346

SBL + 67.050
1.300

0.900
+ 66.150
0.600
+ 65.550

Depth of flow in stream

2.596

Average length of pier

1.30

m
m

0.000

Depth of pier from SBL to the top of foundation

0.90

m
2

Moment at +

66.150

M1

7.733 t-m

M2

1/2 x (

1/2 x

2.596

) x

2.596

0.900 x

1.30

3
2

=
M1 - M2

2.346

)x (

6.017 t-m

1.716

2.346

0.900 )x

1.30

t-m
2

Moment at

65.550

1/2 x

M1

M2

1/2 x

8.164 t-m

2.596

2.346

) (

2.596

/3 +

1.50

)x

1.30

) (

2.346

/3 +

1.50

)x

1.30

10.361 t-m
2
0

2.198 t-m

Govering moments @

M1 - M2

66.150 =

1.716 t-m

Govering moments @

65.550 =

2.198 t-m

12.7.0 Direct loads

With out Buoyancy

1) Dead load from super structure

2) Dead load of hammer head
3) Dead load of bearing pedestal

With 15 % Buoyancy

73.561

73.561

8.669

8.669

1.25

1.25

4) Live load

27.017

27.017

5) weight of column

19.993

18.793

III - 24

6)Change in vertical reaction due to breaking force

Ttal direct loads
Sno

Vertical loads and moments

Loads with out

1.813

1.813

132.30

131.10

with 15 % buoyancy Lontudinal moment

From super strucure

Bearing pedestals

Bed blocks

Live loads

Live load eccentricity

Effect of transverse eccentricity

Braking force (Momnt)

Water currents

3.288

wind force

28.36

132.30

131.10

23.563
0.883
28.5285

Resultant with out wind effect =

132.303

131.10

26.851

Resultant with wind effect =

132.303

131.10

55.215

Resultent B .M with out wind effect

Bending moment with buoyancy

26.851

31.128 =

2
Bending moment with out buoyancy

Transverse

23.563

1.716
31.128

41.108

t-m

37.686

t-m

2
+

29.412 =

0.000
Resultan BM with wind effect
Bending moment with buoyancy

0.000
=

2
55.215

2
+

31.128 =

63.385

t-m

0.000
Bending moment with out buoancy

2
51.927

2
+

29.412 =

59.678

t-m

0.000
12.7.2 tabulation of loads & moments on top of soil
Weight of footing

25.834

Weight of footing with 100% buoyancy

15.501

Total weight of foundation (including dead and live load ) with out buoyancy

158.137

Total weight of foundation (including dead and live load ) with buoyancy

146.604

Sno
1

Vertical loads and moments

with out

with 15 % buoyancy

Longitudinal moment

Transverse

From super structure

Bearing pedestal
Bed block

158.137 146.604

Live load
2

Effect of transverse eccentricity

23.563

Braking force

Water currents

4.038

Effect of wind force

30.34

0.883
31.0365

Resultant with out wind effect =

158.137 146.604

27.601

Resultant with wind effect =

158.137 146.604

57.943

Resultent B .M with out wind effect

Bending moment with buoyancy

27.601

Bending moment with out buoyancy

23.563

2.198
34.117

2
+

34.117

31.920

43.884

t-m

39.675

t-m

2
0.000

Resultan BM with wind effect

Bending moment with buoancy

0.000
=

2
57.943

2
+

34.117

67.242
0.000

Bending moment with out buoancy

2
III - 25

t-m

53.906

31.920

with out wind effect

A) When the canal is empty & Traffic allowed on the Road
Stresss in the column base
=

132.303

37.686

1.423

0.242

92.98 +

Max

248.56 t/m2

155.6

Min

-62.59 t/m2

Stress on soil
158.137 +

39.675

18.098

10.859

8.738 +
Max

12.392

Min

5.084

3.654

B)When canal is running full and traffic allowed on the road

Stresss in the column base
=

131.103

41.108

1.423

0.242

92.14 +

Max

261.84 t/m2

169.7

Min

-77.56 t/m2

Stress on soil
146.604 +

43.884

18.098

10.859

8.101 +
Max

12.142

Min

4.059

4.041

With wind effect

Stresses in the column at the base i.e , on foundation soil
A)When the canal is empty & traffic allowed on the road
Stress in the column at base
=

132.30

59.678

1.423

0.242

92.98 +

246.4

Max

339.34 t/m

Min

-153.38 t/m2

Stress on soil
158.137 +

62.647

18.098

10.859

8.738 +
Max

14.507

Min

2.969

5.769

B)When canal is running full and traffic allowed on the road

Stresss in the column base
=

131.103

1.423

Max

92.14 +

353.80 t/m2

63.385
0.242
261.7
III - 26

62.647

t-m

Min

-169.52 t/m2

Stress on soil
146.604 +

67.242

18.098

10.859

8.101 +

6.192

Max

14.293 t/m2

Min

1.908 t/m2

Direct stress calculated

Direct stress allowable

Bending stress calculated

132.303

92.982 t/m2

1.423
500 t/m2
41.108

(IRC -21,clause 303)

169.699 t/m2

0.242
bending stress allowable

667 t/m2

(IRC -21,clause 303)

As per para 306.5.3, as per IRC 21-2000and as per para B-4- 4.1 the direct and bending stresses calculated shall satisfy the
Direct stress calculated

Bending stress calculated

Direct stress allowable

=

following conditions

bending stress allowable

92.982

169.699

500

667
0.186

0.2544

0.440 <

Hence O.K

Check the load carring capacity of the column

Slenderness ratio

Ie/radius of gyration

Ie=

9.391 <

6.83

radius of gyration =

0.7267

12 Short column

As per code clause 306.1

it is a pedestal column.In pedestal column the cross sectional area of longitudinal

reinforce ment shall not be less than 0.15 % gross sectional area of column. Hence 0.8 % is provided.
P = Ac x cc + sc x Asc
where sc =

1900 Kg / cm2

where cc =

50 Kg / cm2

Ac =

D2 - Asc
13273.23 -

assuming 0.8 % of bd
Ac

106.186 cm2

13167.04 cm2
860105.24 Kg

=
Area of steel

Asc

Area of steel

860.11 t

>

132.303 Hence ok

106.186 cm2

number of 25 mm dia required

21.632

say

22 numbers

Lateral ties
according to the IS 456:2000 the diametre of the lateral ties shall not be less than
1)

1/4 th the diameterof the longitudinal bar

2)
There fore provide

6 mm
8 mm as the diameter of tie bar

pitch of lateral reinforcement should be least of the following

1)

Least lateral dimension of compression member

2) sixteen times the smallest diameter of then longitudinal bar

3)

300 mm

Pitch of transverse ties

Least of the following
1)

130 cm

2)

40 cm

3)

30 cm
III - 27

Pitch of ties

30 cm

Distribution steel

8 mm @

300 mm c/c

13.0 Design of Hammer Head

h=

5.0

0.25
b

0.70 a
c.g of cantilever portion = h - (( 2a+b)/(a+b))x h/3
1.85

1.3

h
Load on column due to super structure

Load due to bearing pedestal

1.250 t

Live load reaction on hammer head

27.017 t

101.828 t

Total
Length of hammer head

Load per m run

length of over hanging portion

73.561 t

5 m
20.37 t/m

1.85 m

34.851 m

Self weight of cantilever portion of hammer head

2.86 t

dist.of C.G of this load from column face

0.779 m

B.M due to self weight

2.225 t-m

Total B.M

37.075 t-m

Cantilever B.M at the face of the column

wl2/2

Using M 20 and Fe 415 grade

m

13

70 kg/cm2

1900 kg/cm2

cleatr cover =

50

mm

0.324

Dia of bar

20

mm

0.892

10.11

Required depth

Effectve depth =

53.112 cm

70

64.00 cm

<

64.00 cm

-1.00

Qb
fy =
area of steel required

Minimum steel

tx jxd

3707526 =
108467.2

As/bd=0.85/fy

0.85

as per para265.1.1 of is 456-2000

=
Provide

415

34.181 cm2
x

1300

x 700 =

1863.86 mm2

415
18.64

cm2 <

34.181 cm2

20 mm dia bars

12 bars

There fore area provided =

37.68 cm2

% of steel

0.4529 %

Shear stress allowable with out shear reinforcement =

c=

2.8492 Kg/cm2

check for shear

Shear force = V

self weight hammer head

20.37

1.85

37.676

(From super structure )

2.86 t

Cantilever portion of hammer head

Total

balance shear

40.532 t
4.87 Kg/cm2
2.022 x

>

2.849 kg/cm2 ( Hence shear reinforce ment is required )

130 x

64.00 =
III - 28

16826.7 kg

Vertical stirrups =

Vs =

Sv a sv d

8 mm dia assumed

Sv
Sv

Asv

2300 Kg /cm2
4 x

2
3.14 x

0.8

2.0096 cm2

4
Sv

2300 x

2.0096

64.00 =

17.580 cm

16826.7
provide

mm 4 legged stirrups @

12 cm c/c.

Side face reinforce ment

Through the depth of the beam is less than 750 mm provide 0.1 % of side face reinforcement.
=
Area of

11.7 cm2

16 mm dia bars
number of bars

As per clause 26.5.1.3

of IS 456 - 2000 Side face reinforcement is required

2.0096 cm2

6 nos

provide 3 nos on each side

Provide side face reinforcement Through the depth is less than 750 mm .

Design of footing
Load from super structure

73.561 t

Weight of hammer head

8.669 t

self weight of column

19.993 t

Weight of footing

25.834 t

Total weight

129.307 t

Liveload reaction

27.017 t

Total load

156.325 t

Provide side of footing

Weight of bearing pedestal

1.25 t

4.8 m
max

14.507 t/m2

min

2.969 t/m2

r
1.30

1.75

R
14.507

4.8
2.969
1.75

4.8
=

11.539

4.8
x

stress at the face of column

3.05

7.332
10.300 t/m2

R = Radius of footing

2.4 m

r= Radius of column

0.65 m

m2

4.8 m

Check for depth of footing

2

0.6 R 2 + r 2 + R r

0.6

R+r
=

1.523 m

Area shaded =

4
Load on shaded area =
Maximum bending moment =

2.4

+0.65

2.4

- 0.65

4
10.300 x

4.192 =

43.180 x

1.523 =

Breadth of shaded part at column face

43.180 t
65.768 t-m
1.3

4
Adopting C =

+0.65 +2.4x 0.65

R2 - r2

2.4

7 N/mm2

t =

190 N/mm2

and equating the moment of resistence to the maximum B.M =

III - 29

1021 mm

4.192

10.11 bd2

10.11 x

d=
provide

25.241

1021.0 d2
cm

<

65.77 x 1000x100

60.00 cm

20 mm dia bars with a clear cover of

60 mm

Effective cover to the centre of the upper layer =

Effective depth =

60

+20

+10.00

90.00 mm

510 mm

Punching shear consideration

Punching load = soil reaction on column area

2

10.300

182.97 t

Safe punching shear stress =

x (

4.80

0.65

12 kg/cm2

Equating the punching resistance to the punching load

x

130 x D

D
Steel required for the footing

x 12.00 =

182973.45

37.335 cm

65.768

x 1000

1900

x 0.892

There fore provide

24.00

bars of

x 100 =

76.090 cm2

x51.00

20 mm dia in both ways

The reinforcement to the above extent should be provided in two principle direction and in a width equal to the sides of squence
inscribed in the plan of the footing. Length of the side of the inscribed in the plan of the footing. Length of the sides
of the inscribed square
R 2=

2.40 2 =

or

3.3941 m

3394.0 mm

Check for one way shear

The critical section for one way shear is taken at a distance equal to the effective epth from the column face
The depth of footing at the edge
300.00

0.30 m
x=

87.429

510
600 -

1.3

87.43 =

Effective depth at critical depth

513 mm

513

=
Radius at the critical section

90.00

0.30

650.0 +

1160.0 mm

510

2
=
=

x 116.00

0.65

=
=

x 42.3

0.0056 kg/cm2
24.00

3.140

116.0

x 42.3

2
stress

4.8

2.4

x
stress allowed with out shear reinforcement

0.30

r+ d

10.3004 (

percentage of steel at the critical section

510
-

422.6 mm

Nominal shear stress at the critical sec tion

=

1750

1160

1750

1.30
x 100

0.9787 %
3.874 kg/cm2

>
0.006

III - 30

kg/cm2

14. DESIGN OF SLOPED STREAM WING WALLS

unit wt of concrete
unit wt of earth

=
=

2.400
2.100

t
t

0.5

W4

TBL

73.640

W5

W2

+ 71.15
stressmax min
16.782

9.470

stressmax min
16.805

10.788

W1

1
5
W3

W3'
0.30

0.82

3.05

+ 67.050

SB

W4'
1.000

1.820

0.50
4.050
W6
4.65

1.730 B 0.30
C

+ 66.050
0.5
+ 65.550

III - 31

15.DESIGN OF WINGS & RETURN WALLS

1) DESIGN OF RETURN WALL - U/S & D/S

unit wt of concrete =
2.400 t
unit wt of earth
=
2.100 t
+
70.870
W3
W6

W1
w4'
W2

0.764

4.820
67.05

0.300
0.936
B
2.200
W7
C
2.800

0.654

stressesmax min
16.434

5.058

SBL

A
w5
0.500

stressesmax min
20.514

1.000
0.30
+

66.050

0.50

III - 32

65.550

16.DESIGN OF CANAL WING AT STARTING & RETURN WALLS

unit wt of concrete

2.400 t

section 9-9

unit wt of earth
= 2.100 t
surcharge load
= 1.200 t
CALCULATION OF STRESSES IN CONCRETE :
0.5 +

73.640

73.04

TBL

W3
W5

FSL

W1
stresses at Base
max
W2
1.850
Pva
w5'' + 71.790

PV
A
1.000 0.500
W4

Ph

w5'

0.30 B

CBL

-5.100
min
1.236

+ 5.740 Pha
w5'''
0.30
66.050

1.7
3.200
W6
3.800

41.209
stresses on soil
max
36.629

min

0.5
+ 65.550

17.DESIGN OF CANAL WING AT END

unit wt of concrete
unit wt of earth
surcharge load

=
=
=

2.400 t
2.100 t
1.200 t

0.5 +

73.640

73.04

TBL

w4
w6'

FSL

W1

stresses at Base
max
69.829
W2

w6

stresses on soil

PV
A

0.600

0.500

B
0.30
C

2.856
3.86
W5
4.456

max
63.323

w4'' Pva
CBL +
w4'''

1.756
W3

Ph

min
-3.328

W4'
1.0

71.790

5.740
0.3

Pha
66.050
0.5

+ 65.550

III - 33

min
0.937

18.DESIGN OF CANAL WING AT STARTING & RETURN WALLS

unit wt of concrete
unit wt of earth
surcharge load

=
=
=

section 9'-9'

2.400 t
2.100 t
1.200 t

0.5 +

73.640

73.04

with out surcharge load

TBL

W3
W5

FSL

W1

stresses at Base
max
45.721

W2

stresses on soil
1.850
pva
w5'' + 71.790
w5'''

A
1.000 0.500
pv
W4
w5'

ph

min
-7.910

0.30 B

1.0

0.30

2.500
W6
3.100

max
38.136

min
0.894

CBL

5.740
pha
66.050
0.5

+ 65.550

19.DESIGN OF CANAL WING AT END

section 8'-8'
with out surcharge load

unit wt of concrete
= 2.400 t
unit wt of earth
= 2.100 t
surcharge load
= 1.200 t
CALCULATION OF STRESSES IN CONCRETE :

w4

0.5 +

73.640

73.04

w6'

TBL
stresses at Base
max

FSL

W1

38.524

min
-4.150

stresses on soil
max
W2

w6

0.600 0.500

W4'

2.856

0.3
3.16

pva
CBL +
w4''

1.756
W3

B
0.30

35.196

W5
3.756

w4'''
0.3

71.790
5.740
pha
66.050

0.5
+ 65.550

III - 34

min
2.116