Design of Wingwall at Chainage

4.635 0.45

F.L 390.369

D =

4

.635

H = 1.5

A A R L 388.869

D = 4.635

(S+V)surcharge on BB

(S+V)surcharge on CC H1 = 8.869

(S+V)surcharge on DD

B B R L 381.500

H2 = 1.800

C R L 379.700

D 379.300

L1 L2 L3 L4 L5 L6 L7

0.4 1.800 1.026 0.45 1.026 1.800 0.4

12.61° ( F.L 390.369

2 1 2 H = 1.5

A' 3 R L 388.869

L8 L9

7 3

H5 = 8.869 5

Earthfill H1 = 8.869

4 5

6

R L 381.500 B' 1.026 1.026 B R L 381.500

6 4

H4 = 1.800 8 7 H2 = 1.800

L10 9 10 379.700

H3 = 0.40 11 379.300

D' D

L1 L2 L3 L4 L5 L6 L7

0.4 1.800 1.026 0.45 1.026 1.800 0.4

6.902

P2=

= 0

C' C

1 H1 = 8.869

H1 A' 2 3

L9

= ###

H5 = 8.87

H2 = 379.700

6 5

3

381.500 1.026

H6 = #REF! B' 8 7 1.8 B

L10 10 H3 = 0.40

H4 = #REF! H4 =###

P1 x K1 D' D 0.000

L1 L2 L3 L4 L6 L7 L8

H1 = 8.869

A A'

#REF!

###

H5 - H1

#REF!

B' H6 - H3

H6 #REF! H3

H4 #REF! H4

1 in

0

1 in 0

C' C

C'

#REF! D'

C'

S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS

62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705

.5

Designed By : Archana V . Kanwaloo.

NAME OF WORK : CONSTRUCTION OF 3/12.20 M PSC GIRDER BRIDGE AT CHAINAGE 47555.50

Date: 09/07/2002 DESIGN OF WING WALL Design Sheet no.:

Revision: MAXIMUM SECTION Note no.:

1 SELF WEIGHT OF WING WALL AND IT'S MOMENTS ABOUT A, B, C & D.

Section of Wing Wall: -

H = 1.500

H1 = 8.869

H2 = 1.800

H3 = 0.400

H4 = 1.800

H5 = 8.869

L1 = 0.400 L2 = 1.800

L3 = 1.026 L4 = 0.450

L5 = 1.026 L6 = 1.800

L7 = 0.400 L8 = 0.159

L9 = 0.1588 L10 = 0.0000

w for Section A - A = L9 + L4 + L8 = 0.768

w for Section B - B = L10 + L3 + L4 + L5 = 2.502

w for Section C - C = L2 + L3 + L4 + L5 + L6 = 6.102

w for Section D - D = L1 + L2 + L3 + L4 + L5 + L6 + L7 = 6.902

( F.L 390.369

2 1 2 H = 1.5

A' R L 388.869

L8 L9

7 3

H5 =8.869 5

H1 =

4 5

6

B' 1.026 B

6 4

H4 = 1.800 8 7 H2L10

9 10 379.700

H3 = 0.4011

379.300

D' D

L1 L2 L3 L4 L6 L7

0.4 1.800 1.026 0.45 1.800 0.4

1.026R L 381.500 R L 381.500

1.026

Earthfill 8.869

= 1.800

L5

12.61°

3

C' C

A4

user 4: Revised as per given level = 379.30



.6





1 SELF WEIGHT OF WING WALL AND IT'S MOMENTS ABOUT A, B, C & D.

Sr. Area Weight Lever Arm Moment

Section A' - A Area x Density x Length Moments about A

1 0.5 x (1.5 - 0.15) x L8 0.107 0.107 x 2.3 x 1.00 L9 + L4 + 0.33L8 = 0.662 = 0.163

= 0.2466

2 1.5 x L4 = 0.675 0.675 x 2.3 x 1.00 L9 + 0.5L4 = 0.384 = 0.596

= 1.5525

3 0.5 x (1.5 - 0.15) x L9 = 0.107 0.107 x 2.3 x 1.00 0.67 x L9 = 0.106 = 0.026

= 0.2466

Total = 2.046 Total = 0.79

Section B' - B Moments about B

1+4 0.5 x L3 x (H5 - 0.15) = 4.472 4.472 x 2.3 x 1.00 L5 + L4 + 0.33L3 = 1.814 = 18.660

= 10.2852

2+5 L4 x H1 = 3.991 3.991 x 2.3 x 1.00 L5 + 0.5L4 = 1.251 = 11.481

= 9.1794

6 0.5L5 (H1 - 0.15) = 4.472 4.472 x 2.3 x 1.00 0.67 x L5 = 0.684 = 7.037

= 10.2852

7 L3 (H4 - H2) = 0.000 0.000 x 2.3 x 1.00 L5 + L4 + 0.5L3 = 1.989 = 0.000

= 0.0000

8 0.5 x L10 x (H4 - H2) = 0.000 0.000 x 2.3 x 1.00 L5 + L4 + L3 + 0.33L10 = 2.50153 = 0.000

= 0.0000

Total = 29.75 Total = 37

Section C' - C Moments about C

1+4 0.5 x L3 x (H5 - 0.15) = 4.472 4.472 x 2.3 x 1.00 L6 + L5 + L4 + 0.33L3 = = 37.173

= 10.2852 3.614

2+5 L4 x H1 = 3.991 3.991 x 2.3 x 1.00 L6 + L5 + 0.5L4 = 3.051 = 28.004

= 9.1794

6 0.5L5 (H1 - 0.15) = 4.472 4.472 x 2.3 x 1.00 L6 + 0.667L5 = 2.484 = 25.550

= 10.2852

7 L3 (H4 - H2) = 0.000 0.000 x 2.3 x 1.00 L6 + L5 + L4 + 0.5L3 = = 0.000

= 0.0000 3.789

8 0.5 x L2 x H4 = 1.620 1.620 x 2.3 x 1.00 L6 + L5 + L4 + L3 + 0.33L2 = 18.261

= 3.7260 = 4.90093

9 (L3 + L4 + L5) x H2 = 4.503 4.503 x 2.3 x 1.00 L6 + 0.5(L3 + L4 + L5) = = 31.595

= 10.3563 3.051

10 0.5 x L6 x H2 = 1.620 1.620 x 2.3 x 1.00 0.667 x L6 = 1.2006 = 4.473

= 3.7260


Section D' - D Moments about D

1+4 0.5 x L3 x (H5 - 0.15) = 4.472 4.472 x 2.3 x 1.00 L7 + L6 + L5 + L4 + 0.33L3 = 41.287



.7





= 10.2852 = 4.014

2+5 L4 x H1 = 3.991 3.991 x 2.3 x 1.00 L7 + L6 + L5 + 0.5L4 = = 31.676

= 9.1794 3.451

6 0.5L5 (H1 - 0.15) = 4.472 4.472 x 2.3 x 1.00 L7+ L6 + 0.667L5 = 2.884 = 29.664

= 10.2852

7 L3 (H4 - H2) = 0.000 0.000 x 2.3 x 1.00 L7 + L6 + L5 + L4 + 0.5L3 = = 0.000

= 0.0000 4.189

8 0.5 x L2 x H4 = 1.620 1.620 x 2.3 x 1.00 L7 + L6 + L5 + L4 + L3 + 0.33L2 = 19.751

= 3.7260 = 5.30093

9 (L3 + L4 + L5) x H2 = 4.503 4.503 x 2.3 x 1.00 L7 + L6 + 0.5(L3 + L4 + L5) = 35.737

= 10.3563 = 3.451

10 0.5 x L6 x H2 = 1.620 1.620 x 2.3 x 1.00 L7 + 0.667 x L6 = 1.6006 = 5.964

= 3.7260

11 (L1 + L2 + L3 + L4 + L5 + L6 2.761 x 2.3 x 1.00 0.5 x (L1 + L2 + L3 + L4 + L5 = 21.910

+ L7) x H3 = 2.761 = 6.3494 + L6 + L7) = 3.451

Total = 54 Total = 186

SELF WEIGHT OF EARTHFILL AND IT'S MOMENTS ABOUT A, B, C & D.

Sr. Area Weight Lever Arm Moment

Section A' - A Area x Density x Length Moments about

A

1 L8 x 0.15 = 0.024 0.02382 x 1.76 x 1.00 L9 + L4 + 0.5L8 = 0.688 = 0.029

= 0.042

2 0.5(H - 0.15)L8 = 0.107 0.11 x 1.8 x 1.00 L9 + L4 + 0.667L8 = = 0.135

= 0.189 0.715

3 0.5 x L8 x L8 Tan(12.61)° = 0.003 x 1.8 x 1.00 L9 + L4 + 0.667L8 = = 0.004

0.003 = 0.0050 0.715

Total = 0.236 Total = 0.17

Section B' - B Moments about

1 H5 x L10 = 0.000 0.000 x 1.8 x 1.00 L5 + L4 + L3 + 0.5L10 = = 0.000

= 0.000 2.502

2 0.5 x (L10 + L3)² x Tan 12.61º 0.118 x 1.8 x 1.00 L5 + L4 + 0.667(L10 + L3) = = 0.447

= 0.118 = 0.2071 2.160

3 0.5 x L10 x (H4 - H2) = 0.000 0.000 x 1.8 x 1.00 0.667L10 + L3 + L4 + L5 = = 0.000

= 0.0000 2.502

4 0.5L3 x (H5 - 0.15) = 4.472 4.472 x 1.8 x 1.00 0.667L3 + L4 + L5 = 2.160 = 17.000

= 7.8704

5 L3 x 0.15 = 0.154 0.154 x 1.8 x 1.00 0.5L3 + L4 + L5 = 1.989 = 0.539

= 0.2708


Section C' - C Moments about

C



.8





1 L2 x H5 = 15.964 15.964 x 1.8 x 1.00 0.5L2 + L3 + L4 + L5 + L6 = 146.147

= 28.097 = 5.202

2 0.5 x L2 x H4 = 1.620 1.620 x 1.8 x 1.00 0.667L2 + L3 + L4 + L5 + L6 = 15.688

= 2.8512 = 5.502

3 L3 x 0.15 = 0.154 0.154 x 1.8 x 1.00 0.5L3 + L4 + L5 + L6 = = 1.026

= 0.2708 3.789

4 0.5 x L3 x (H5 - 0.15) = 4.472 4.472 x 1.8 x 1.00 0.667L3 + L4 + L5 + L6 = = 31.166

= 7.8704 3.960

5 0.5 x (L2 + L3)² x Tan 12.61º 0.893 x 1.8 x 1.00 0.667(L2 + L3) + L4 + L5 + L6 = 8.112

= 0.893 = 1.5720 = 5.161


Section D' - D Moments about

D

1 L1 x (H5 + H4) = 4.268 4.268 x 1.8 x 1.00 0.5L1+ L2 + L3 + L4 + L5 + L6 + L = 50.335

= 7.511 = 6.702

2 L2 x H5 = 15.964 15.964 x 1.8 x 1.00 0.5L2 + L3 + L4 + L5 + L6 + L7 = 157.386

= 28.097 = 5.602

3 0.5 x L2 x H4 = 1.620 1.620 x 1.8 x 1.00 0.667L2 + L3 + L4 + L5 + L6 + L7 = 16.828

= 2.8512 = 5.902

4 L3 x 0.15 = 0.154 0.154 x 1.8 x 1.00 0.5L3 +L4 + L5+ L6 + L7 = = 1.134

= 0.2708 4.189

5 0.5 x L3 x (H5 - 0.15) = 4.472 4.472 x 1.8 x 1.00 0.667L3 + L4 + L5 + L6 + L7 = 34.315

= 7.8704 = 4.360

6 0.5 x (L1+ L2 + L3)² x Tan(12.61)° 3.755 x 1.8 x 1.00 0.667(L1 + L2 + L3) + L4 + L5 + = 38.507

= 3.755 = 6.6079 L6 + L7 = 5.827


Calculation of Earth Pressures on Wing Wall with Surcharge :

ZONE 1



.9





12.61º (L3/H5) = 6.60º

= 0.12

35º 11.67º

= 0.611 = 0.20

Cos² 28.40º = 0.774 = 0.774

Sin 46.7º = 0.727 0.99 x 0.95 1 + 0.73 x 0.38

Sin 22.39º = 0.381 0.95 x 0.99

Cos 18.26º = 0.950 = 0.774

Cos -6.01º = 0.994 0.937 1 + 0.277

Cos² 6.60º = 0.987 0.944

* Cos 18.26º

* Sin 18.26º = 0.774

* Required for Calculation of vertical and 0.937 ( 1 + 0.542)

Horizontal components

= 0.774 = 0.347

0.937 x 2.377

ZONE 2

12.61º (L2/H4) = 45.00º

= 0.785

35º 11.67º

= 0.611 = 0.20

Cos² -10.00º = 0.970

Sin 46.67º = 0.727 = 0.970

Sin 22.39º = 0.381 0.50 x 0.55 1 + 0.73 x 0.38

Cos 56.67º = 0.550 0.55 x 0.84

Cos 32.39º = 0.844 = 0.970

Cos² 45.00º = 0.500 0.275 1 + 0.277

* Cos 56.67º 0.464

* Sin 56.67º

= 0.970


Horizontal components

= 0.970 = 1.123

0.275 x 3.143

Zone 3

12.61º (L1/0) = 0.0º = 0.00

35º 11.67º

i1 = q1 = tan-1

K1 = Cos² (f - q)

f = d1 = Cos² q Cos (q + d) 1 + Sin (d + f) Sin (f - i)

Cos (q + d) Cos (q - i)

Cos² (f - q)

Sin (d + f)

Sin (f - i)Cos (q + d)

Cos (q - i)Cos² qCos (q + d )

Sin (q + d )

i2 = q2 = tan-1

f = d2 = K2 = Cos² (f - q)

Cos² q Cos (q + d) 1 + Sin (d + f) Sin (f - i)


Cos²(f - q)

Sin(d + f)



Sin (q + d )

i3 = q3 = tan-1

f = d3 = K3 = Cos² (f - q)

2

2

2

2

2

2

2

2

2



.10





= 0.611 = 0.204

Cos² 35.00º = 0.671

Sin 46.67º = 0.727 = 0.671

Sin 22.39º = 0.381 1.00 x 0.98 1 + 0.73 x 0.38

Cos 11.67º = 0.979 0.98 x 0.98

Cos -12.61º = 0.976 = 0.671

Cos² 0.00º = 1.000 0.979 1 + 0.277

* Cos 11.67º 0.956

* Sin 11.67º = 0.671


Horizontal components = 0.671 = 0.289

0.979 x 2.367

Earth Pressure due to Surcharge on Wing Walls

12.61º 35º 1.76 T/m³ S = 13.70

V = 5.50 B = 3 m L = 6.85

center line of track

Refer IRS Substructure Code para 5.8.3 3.425

Height of Wall at Section 'A - A' (h) = H + 0.33 = 1.833 26.56°

Height of Wall at Section 'B - B' (h) = H5 + H4 - H2 + 0.33 = 9.202 1

Height of Wall at Section 'C - C' (h) = H4 + H5 + 0.33 = 10.999

Height of Wall at Section 'D - D' (h) = H3 + H4 + H5 + 0.33 = 11.40 2

Height (h1) for Section 'A - A' = 1.833 - 4.476 = -2.643 Say 0.00 wing

Height (h1) for Section 'B - B' = 9.202 - 3.609 = 5.593

Height (h1) for Section 'C - C' = 10.999 - 1.809 = 9.190

Height (h1) for Section 'D - D' = 11.399 - 1.409 = 9.990

Calculation of 'D' at bottom of sleeper = L - B + 0.33 = 4.635

2 x Sin(26.56) °

Calculation of 'D' for Section 'A - A' = L - B - L8 + 0.33 = 4.476

2 x Sin(26.56) °

Calculation of 'D' for Section 'B - B' = L - B - L3 - L10 + 0.33 = 3.609

2 x Sin(26.56) °

Calculation of 'D' for Section 'C - C' = L - B - L2 - L3 + 0.33 = 1.809

2 x Sin(26.56) °

Calculation of 'D' for Section 'D - D' = L - B - L1 - L2 - L3 + 0.33 1.409

2 x Sin(26.56) °

P1 = (S + V) h1 x Ka act at h1

B + 2D 2

Section A-A

P1 = (S + V) x h1 x K1

Cos² q Cos (q + d) 1 + Sin (d + f) Sin (f - i)


Cos²(f - q)

Sin (d + f)



Sin (q + d )

a = f = w = T/m2

T/m2

2

2

2

2



.11





B + 2D

= 13.70 + 5.5 x 0.0 x 0.35 Acts at h1/2 = 0.0 = 0.00

3.0 + (2.0 x 4.476) 2

= 0.000

Section B-B

P1a = (S + V) (h1 - (H4 - H2) x K1

B + 2D

= 13.70 + 5.5 x (5.6 - (1.80 - 1.80) x 0.35 Acts at H5/2 = 8.87 = 4.4345

3.0 + (2.0 x 3.609) 2

= 3.651

P1b = (S + V)((H4 - H2) x K2

B + 2D

= 13.70 + 5.5 x (1.8 - 1.8) x 1.12 Acts at H5/2 = 8.9 = 4.4345

3.0 + (2.0 x 3.609) 2

= 0.000

Section C - C

P1a = (S + V) (h1 - H4) x K1

B + 2D

= 13.70 + 5.5 x (9.2 - 1.80) x 0.35 Acts at H5/2 = 8.9 = 4.4345

3.0 + (2.0 x 1.809) 2

= 7.447

P1b = (S + V) x H4 x K2

B + 2D

= 13.70 + 5.5 x 1.8 x 1.12 Acts at H4/2 = 1.80 = 0.9

3.0 + (2.0 x 1.809) 2

= 5.865

Section D - D

P1a = (S + V) (h1 - H4 - H3) x K1

B + 2D

= 13.70 + 5.5 x (10.0 - 1.80 - 0.40) x 0.35 Acts at H5/2 = 8.9 = 4.4345

3.0 + (2.0 x 1.409) 2

= 8.930

P1b = (S + V) x H4 x K2

B + 2D

= 13.70 + 5.5 x 1.80 x 1.12

3.0 + (2.0 x 1.409) Acts at H4/2 = 1.8 = 0.9

= 6.671 2



.12





P1c = (S + V) x H3 x K3

B + 2D

= 13.70 + 5.5 x 0.40 x 0.29 Acts at H4/2 = 1.80 = 0.9

3.0 + (2.0 x 1.409) 2

= 0.382

Earth Presure due to Surcharge as per para 5.8.4.

P2 = ½ wh (h + 2h3) x Ka acts at h/3

Height for Section A - A (h) = H + L8 x Tan (12.6)° = 1.536

Height for Section B - B (h) - (I) = H5 + L3 x Tan (12.6)° = 9.098

Height for Section B - B (h) - (II) = (H4 - H2) + (L3 + L10) Tan (12.6)° - L3Tan (12.6)° = 0.000

Height for Section C - C (h) - (I) = H5 + L3 x Tan (12.6)° = 9.098

Height for Section C - C (h) - (II) = H4 + (L2 + L3) x Tan (12.6)° - L3Tan (12.6)° = 2.203

Height for Section D - D (h) - (I) = H5 + L3 x Tan (12.6)° = 9.098

Height for Section D - D (h) - (II) = H4 + (L2 + L3) x Tan (12.6)° - L3Tan (12.6)° = 2.203

Height for Section D - D (h) - (III) = H3 + (L1 + L2 + L3) Tan (12.6)° - (L3 + L2) Tan = 0.489

(12.6)°

h3 =

= 1 x Cot 35º x Tan 12.61º x h

3

= 1 x 1.428 x 0.224 x h

3

= 0.106 h

h3 for Section A - A = 0.106 x 1.54 = 0.16

h3 for Section B - B - (I) = 0.106 x 9.10 = 0.97

h3 for Section B - B - (II) = 0.106 x 0.00 = 0.00

h3 for Section C - C - (I) = 0.106 x 9.10 = 0.97

h3 for Section C - C - (II) = 0.106 x 2.20 = 0.23

h3 for Section D - D - (I) = 0.106 x 9.10 = 0.97

h3 for Section D - D - (II) = 0.106 x 2.20 = 0.23

h3 for Section D - D - (III) = 0.106 x 0.49 = 0.05

Earth Pressure Calculations:- PRESSURE DIAGRAM

Intensity of Earth Pressure at A-A (X1)

=

= 0.347 x 1.8 (1.54 + 2 x 0.16)

= 1.139

A A

Intensity of Earth Pressure at B-B at the end of Zone I - (X2) X1

1/3 x Cotf x Tana x h

K1 x w (h + 2h3)



.13





=

= 0.347 x 1.8 (9.10 + 2 x 0.97)

= 6.748 X2

B X3 B

Intensity of Earth Pressure at B-B (X3)

= C X4 C

= 0.347 x 1.8 (0.00 + 2 x 0.00)

= 0.000 D X5 D

Intensity of Earth Pressure at C-C (X4)

=

= 0.347 x 1.8 (9.10 + 2 x 0.97) + 1.12 x 1.8 (2.20 + 2 x 0.23)

= 12.030

Intensity of Earth Pressure at D-D (X5)

=

= 0.347 x 1.8 (9.10 + 2 x 0.97) + 1.12 x 1.8 (2.20

+ 2 x 0.23) + 0.29 x 1.8 (0.49 + 2 x 0.05)

= 12.333

Total Pressure at A-A (P2) = ½ x X1 x h

= ½ x 1.139 x 1.54

= 0.874

Total Pressure at B-B (P2a) = ½ x X2 x (H5 + L3 Tan (12.6)°

= ½ x 6.748 x (8.87 + 1.03 x Tan (13)°

= 30.699

(P2b) = X2 + X3 x (H4 - H2 + L10 Tan (12.6)°

2

= 6.748 + 0.00 x (1.80 - 1.80 + 0.00 x Tan (13)°

2

= 0.0000

Total Pressure at C-C (P2a) = ½ x X2 x (H5 + L3 Tan (12.6)°

= ½ x 6.748 x (8.87 + 1.03 x Tan (13)°

= 30.699

(P2b) = X2 + X4 x (H4 + L2 Tan (12.6)°

2

= 6.748 + 12.03 x (1.80 + 1.80 x Tan (12.6)°

2

= 20.6815

Total Pressure at D-D (P2a) = ½ x X2 x (H5 + L3 Tan (12.6)°

= ½ x 6.748 x (8.87 + 1.03 x Tan (12.6)°

K1 x w (h + 2h3)

K1 x w (h + 2h3)

K1 x w (h + 2h3) + K2 x w (h + 2h3)

K1 x w (h + 2h3) + K2 x w (h + 2h3) + K3 x w (h + 2h3)



.14





= 30.699

(P2b) = X2 + X4 x (H4 + L2 Tan (12.6)°

2

= 6.748 + 12.03 x (1.80 + 1.80 x Tan (12.6)°

2

= 20.6815

(P2c) = X4 + X5 x (H3 + L1 Tan (12.6)°

2

= 12.030 + 12.33 x (0.40 + 0.40 x Tan (12.6)°

2

= 5.9627

SECTIONVERTICAL FORCE DUE TO SURCHARGE HORIZONTAL FORCE DUE TO SURCHARGE

P1 Vertical (FV1) P2 Vertical (FV2) P1 Horizontal (FH1) P2 Horizontal (FH2)

A - A'P1 x Sin q1 + d1 P2 x Sin q1 + d1 P1 x Cos q1 + d1 P2 x Cos q1 + d1

= 0.000 = 0.274 = 0.000 = 0.830

B - B'

P1a x Sin q1 + d1 P2a x Sin q1 + d1 P1a x Cos q1 + d1 P2a x Cos q1 + d1= 1.144 = 9.621 = 3.467 = 29.153

P1b x Sin q2 + d2 P2b x Sin q2 + d2 P1b x Cos q2 + d2 P2b x Cos q2 + d2= 0.000 = 0.000 = 0.000 = 0.000

C - C'



D - D'



P1c x Sin q3 + d3 P2c x Sin q3 + d3 P1c x Cos q3 + d3 P2c x Cos q3 + d3= 0.077 = 1.206 = 0.374 = 5.839

Dead Load and Live Load Surcharge

SECTIONV.F H.F

Horizontal Lever Arm (H1) S.M O.M(PV1) (PH1)

A - A 0.000 0.0001.5 = 0.75 L9 + L4 + L8 = 0.6882

0.000 0.0002 2

B - B

1.144 3.467

H4 - H2 + L5 + L4 + L3 = 1.9886

2.27516 9.69379h1 - (H4 - H2) = 2.796 2

2

Vertical Lever Arm(V1)



.15




Revision: MAXIMUM SECTION Note no.:B - B

0.000 0.000H4 - H2 = 0.00 L5 + L4 + L3 + L10 = 2.502

0.000 0.0002 2

C - C

2.334 7.072h1 - H4 + H4 = 5.49479 L6 + L5 + L4 + L3 = 3.789

8.842 38.862 2

4.900 3.223H4 = 0.900 L6 + L5 + L4 + L3 + L2 = 5.20

25.488 2.9012 2

D - D

2.798 8.480

H3 + H4 + L7 + L6 + L5 + L4 + L3 = 4.19

11.722 51.6818h1 - (H4 - H3) = 6.0948 2

2

5.574 3.666H3 + H4 = 1.30 L7 + L6 + L5 + L4 + L3 + L2 = 5.60

31.222 4.7662 2

0.077 0.374H3 = 0.20 L7 + L6 + L5 + L4 + L3 + L2 L1

0.533 0.0752 = 6.902

Earth Pressure and Earthfill Surcharge.

SECTIONVertical Horizontal

S.M O.MForce (PV2) Force (PH2)

A - A 0.274 0.8301.5 = 0.50 L9 + L4 + 0.67L8 =

0.196 0.4153 0.715

B - B

9.621 29.153H4 - H2 + H5 = 2.956 L5 + L4 + 0.67L3 =

20.781 86.23 2.160

0.000 0.000H4 - H2 = 0.00 L5 + L4 + L3 + 0.66

0.000 0.0003 L10 = 2.502

C - C

9.621 29.153H5 + H4 = 3.406 L6 + L5 + L4 + 0.667

38.099 99.33 L3 = 3.960

17.279 11.365H4 = 0.60 L6 + L5 + L4 + L3

95.072 6.8193 0.667L2 = 5.502

D - D

9.621 29.153H5 + H4 + H3 = 5.156 L7 + L6 + L5 + L4 +

41.947 150.33 0.667L3 = 4.360

17.279 11.365H3 + H4 = 1.000 L7 + L6 + L5 + L4 +

101.984 11.363 + 0.67L2 = 5.902

1.206 5.839H3 = 0.13 L7 + L6 + L5 + L4 + L

8.322 0.7793 + L2 + L1 = 6.902

Stabilising moment due to (D.L + L.L) Surcharge:

Vertical Lever Arm(V1)

Horizontal Lever Arm (H1)

0.45

F.L 390.369

1.5

A R L 388.869


(S+V)surcharge on CC H1 =


B B

H2

C R L 379.700

D 379.300

L1 L2 L3 L4 L6 L7

0.4 1.800 1.026 0.45 1.800 0.4

R L 381.500

H =

= 1.800

8.869

D =

4

.635

A

L5

1.026

4.635

D = 4.635



.16





Section A - A:

Section A - A is far away from D.L + L.L distribution line. Hence, Surcharge Load on A - A = 0.00

Section B - B:

1) Intensity of D.L + L.L = L.L + D.L = 13.70 + 5.50 = 1.565 T/m

B + 2D 3.0 + 2 x 4.635

2) Length( D.L + L.L ) Surcharge = L3 - D at Bottom of sleeper - D of Ballast cushion -Thk of coaping

Batter on Earthfill side

= 1.026 - ( 4.635 - 0.33 - 0.15 )

9

= 0.537 m

3) Total load of (L.L + D.L) surcharge = Intensity x Length

= 1.565 x 0.537

= 0.840 T

4) Lever Arm = L5 + L4 + D - 0.15 - 0.33 + Length( D.L + L.L ) Surcharge

Batter at earthfill side 2

= 1.026 + 0.450 + ( 4.635 - 0.15 - 0.3 ) + 0.537

8.5 2

= 2.233 m

5) Moment = Total Load x Lever arm

= 0.840 x 2.233

= 1.876 T m

Section C - C:


B + 2D 3.0 + 2 x 4.635

Length( D.L + L.L ) Surcharge = L2 + L3 - D at botm of sleeper - D of Ballast cushion - Thickness of coaping

Batter at earthfill side

= 1.800 + 1.026 - ( 4.635 - 0.330 - 0.15 )

9

0.45

F.L 390.369

1.5

A R L 388.869


(S+V)surcharge on CC H1 =


B B

H2

C R L 379.700

D 379.300

L1 L2 L3 L4 L6 L7

0.4 1.800 1.026 0.45 1.800 0.4

R L 381.500

H =

= 1.800

8.869

D =

4

.635

A

L5

1.026

4.635

D = 4.635



.17





= 2.337 m

3) Total load of (D.L + L.L) surcharge = Intensity x Length

= 1.565 x 2.337

= 3.657 T

4) Lever Arm = L6 + L5 + L4 + D - 0.15 - 0.33 + Length( D.L + L.L ) Surcharge


= 1.800 + 1.026 + 0.450 + ( 4.635 - 0.15 - 0.3 ) + 2.337

9 2

= 4.933 m


= 3.657 x 4.933

= 18.039 T m

Section D - D:


B + 2D 3.0 + 2 x 4.635

2) Length( D.L + L.L ) Surcharge = L1 + L2 + L3 - D at Botm of sleeper - D of Ballast cushion - Thk of coaping

Batter on Earth fill side

= 0.40 + 1.80 + 1.026 - ( 4.635 - 0.330 - 0.15 )

9

= 2.737 m

3) Total load of (D.L+ L.L) surcharge = Intensity x Length

= 1.565 x 2.737

= 4.283 T

4) Lever Arm = L7 + L6 + L5 + L4 + D - 0.15 - 0.33 + Length( D.L + L.L ) Surcharge


= 0.400 + 1.800 + 1.026 + 0.450 + ( 4.635 - 0.15 - 0.33 ) + 2.737

9 2

= 5.533 m


= 4.283 x 5.533

= 23.696 T m

SUMMARY OF LOADS & BENDING MOMENTS @ SECTION A - A

Sr. No. Loads and Moments due to

1 Self Weight of Wing Wall - 2.046 - 0.785

Horizontal Force (T)

Vertical Load

(T)

Overturning

(Tm)

Stabilising

(Tm)



.18





2 - 0.236 - 0.167

3 0.000 - 0.000

4 0.830 - 0.415 -

5 - 0.000 - 0.000

6 0.274 0.196

7 Vertical Surcharge Load - -

Sum 0.830 2.555 0.415 1.15

Total Vertical Load = 2.555 Tonnes

Net Moment @ base @ 'A - A' (m) =

= -0.733 Tm (Stabilising)

Location of resultant from point A (x) m = 0.733

2.555

= 0.287 meters towards A inside the base

Total width at base of wing wall (w) = 0.768

eccentricity (e) = w - x meters

2

= 0.768 - 0.29 = 0.097 meters

2

Calculation of Base Pressures at Section A - A

Base Area = L x w

= 1.000 x 0.768

= 0.768 m²

Section Modulus = 1 x w² x L = 1 x 0.6 x 1.0 = 0.098 m³

6 6

Direct Stress = Total Vertical Load = 2.555 = 3.329 T/m²

Base Area 0.768

Bending Moment @ at centre line of base of Wing Wall = Vertical load x eccentricity

= 2.555 x 0.097

= 0.248 Tm.

Bending Stress = Moment = ± 0.248 = ± 2.521 T/m²

Section Modulus 0.098

Weight of Earthfill behind Wing Wall

D.LSurcharge + L.L Surcharge (Horizontal Force)

Earth Pressure + Earthfill Surcharge (Horizontal Force)

D.LSurcharge + L.L Surcharge (Vertical Force)

Earth Pressure + Earthfill Surcharge (Vertical Force)

SH = SV = SO = SS =

SV =

SO - SS

SV



.19





Resultant Stress = Direct Stress ± Bending Stress

3.329 ± 2.521

3.329 + 2.521 3.329 - 2.52

5.850 T/m² 0.807 T/m²

SUMMARY OF LOADS & BENDING MOMENTS @ SECTION B - B



2 - 8.348 - 17.986

33.467 - 9.694 -

0.000 0.000

429.153 - 86.185 -

0.000 0.000

5- 1.144 - 2.275

0.000 0.000

6- 9.621 - 20.781

0.000 0.000

7 Vertical Surcharge Load 0.840 1.876

Sum 32.62 49.7 95.9 80.1


Net Moment @ base @ 'B - B' (m) =

= 15.783 Tm (Overturning)

Location of resultant from point B (x) m = 15.783

49.703

= 0.318 meters away from B outside the base


eccentricity (e) = w + X meters

2

= 2.502 + 0.318 = 1.568 meters

2

Calculation of Base Pressures at Section B - B

Base Area = L x w = 1.000 x 2.502 = 2.502 m²


6 6


Base Area 2.502


Vertical Load

(T)

Overturning

(Tm)

Stabilising

(Tm)

Weight of Earthfill behind Wing Wall





SH = SV = SO = SS =

SV =

SO - SS

SV



.20






= 49.703 x 1.568

= 77.950 Tm.




19.869 ± 74.741

19.869 + 74.741 19.869 - 74.74

94.610 T/m² -54.871 T/m²

SUMMARY OF LOADS & BENDING MOMENTS @ SECTION C - C



2 - 40.661 - 202.140

37.072 - 38.859 -

3.223 - 2.901 -

429.153 - 99.304

11.365 - 6.819

5- 2.334 - 8.842

- 4.900 - 25.488

69.621 38.099

17.279 95.072


Sum 50.81 126.0 147.9 533


Net Moment @ base @ 'C - C' (m) =

= -384.854 Tm (Stabilising)

Location of resultant from point C (x) m = 384.854

126.010

= 3.054 meters towards C inside the base


eccentricity (e) = w - x meters = 6.102 - 3.05 = -0.003 meters

2 2

Calculation of Base Pressures at Section C - C

Base Area = L x w = 1.000 x 6.102 = 6.102 m²


6 6


Vertical Load

(T)

Overturning

(Tm)

Stabilising

(Tm)Weight of Earthfill behind Wing Wall





SH = SV = SO = SS =

SV =

SO - SS

SV



.21






Base Area 6.102


= 126.010 -x 0.003

= -0.426 Tm.




20.652 ± 0.069

20.652 + 0.069 20.652 - 0.07

20.721 T/m² 20.584 T/m²

SUMMARY OF LOADS & BENDING MOMENTS @ FOUNDATION LEVEL @ SECTION D - D



2 - 53.208 - 298.505

3

8.480 - 51.682 -

3.666 - 4.766 -

0.374 - 0.075 -

4

29.153 150.321

11.365 11.365

5.839 0.779

5

- 2.798 - 11.722

- 5.574 - 31.222

- 0.077 - 0.533


Vertical Load

(T)

Overturning (Tm)

Stabilising

(Tm)Weight of Earthfill behind Wing Wall






.22





6

- 9.621 - 41.947

- 17.279 - 101.984

- 1.206 - 8.322


Sum 58.88 148.0 219.0 703.9


Net Moment @ base @ 'D - D' (m) = = -484.934 Tm (Stabilising)

Location of resultant from point D (x) m = 484.934

147.954

= 3.278 meters towards D inside the base


eccentricity (e) = w - x meters = 6.902 - 3.28 = 0.173 meters

2 2

Calculation of Base Pressures at Section D - D

Base Area = L x w = 1.000 x 6.902 = 6.902 m²


6 6


Base Area 6.902

Bending Moment @ at centre line of base of WingWall = Vertical load x eccentricity

= 147.954 x 0.173

= 25.620 Tm.




(Foundation - 21.438 ± 3.227

pressures) 21.438 + 3.227 21.438 - 3.23

24.665 T/m² 18.211 T/m²

Factor of Safety against overturning

= Stabilising Moment = 703.92 = 3.214 > 2.0 Hence Safe

Overturning Moment 218.99

Check for Sliding:


SH = SV = SO = SS =

SV =

SO - SS

SV



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0.45 V = 148.0 T H = 58.88 T

Factor of Safety = 0.45 x 148.0 = 1.131 Hence Unsafe

58.88

Hence, provide shear Key.

Passive pressure acting on the section is considered.

Workout details of passive pressure in Zone II.

Passive Pressure Co-efficient (Kp1)

0 (L6/H2) = 45.00º = 0.785

35º 11.67º

= 0.611 = 0.20 1 -

Cos² 80.00º = 0.030

Sin 46.67º = 0.727 = 0.030

Sin 35.00º = 0.574 0.50 x 0.84 1 - 0.73 x 0.57

Cos 33.33º = 0.835 0.84 x 0.71

Cos 45.00º = 0.707

Cos² 45.00º = 0.500 = 0.030

Cos 56.67º 0.418 1 - 0.417

Sin 56.67º 0.591

Required for Calculation of vertical and = 0.030

Horizontal components 0.418 (1 - 0.840)

= 0.030 = 2.832

0.418 x 0.025

Passive Pressure Co-efficient (Kp2) in Zone II

0 (L7/0) = 0.00º = 0.000

35º 11.67º

= 0.611 = 0.20 1 -

Cos² 35.00º = 0.671

Sin 46.67º = 0.727 = 0.671

Sin 35.00º = 0.574 1.00 x 0.98 1 - 0.73 x 0.57

Cos -11.7º = 0.979 0.98 x 1.00

Cos 0.00º = 1.000

Cos² 0.00º = 1.000 = 0.671

Cos 11.67º 0.979 1 - 0.417

Sin 11.67º 0.979

Required for Calculation of vertical and = 0.671

Horizontal components 0.979 (1 - 0.653)

= 0.671 = 5.680

0.979 x 0.121

m =

i = q = tan-1

f = d2 = Kp1 = Cos² (f + q)Cos²q cos(q-d) Sin (d + f) Sin (f + i)

Cos (q - d) Cos (q - i)

Cos²(f + q)Sin(d + f)Sin (f + i)Cos (q - d)

Cos (q - i)

Cos² qCos (q + d )

Sin (q + d )

i = q = tan-1

f = d2 = Kp2 = Cos² (f + q)Cos² q cos(q-d) Sin (d + f) Sin (f + i)

Cos (q - d) Cos (q - i)

Cos²(f + q)Sin(d + f)Sin (f + i)Cos (q - d)

Cos (q - i)

Cos² qCos (q + d )

Sin (q + d )

2

2

2

2

2

2

2

2

2

2

2



.24





Passive Earth Pressure in Zone II = ½ x kp1 x g x (H2²)

= ½ x 2.83 x 1.76 x 3.2 x 0.98

= 7.91 Tonnnes/for full length of Face Wall

Passive Earth Pressure in Zone III = ½ x Kp2 x g x (H3²)

= ½ x 5.68 x 1.76 x 0.16 x 0.98

= 0.783 Tonnnes/for full length of Face Wall

ZONE Vertical Component of Passive Earth Pressure

Passive P1 Sin (q1 + d1 P1 Sin 56.67º P1 Cos (q1+ d P1 Cos 56.67º

Pressure 1 FV1 = 6.607 Tonnes FH1 = 4.346 Tonnes

Passive P2 Sin (q2 + d2 P2 Sin 11.67º P2 Cos (q2+ d P2 Cos 11.67º

Pressure 2 FV2 = 0.158 Tonnes FH2 = 0.767 Tonnes

= 6.765 Tonnes = 5.113 Tonnes

1) Vertical Force to be accounted = 1 x 6.765 = 2.255 T

due to passive pressure 3

2) Horizontal Force to be accounted = 1 x 5.113 = -1.704 T

due to passive pressure 3

3) Self weight = 1.0 x 1.8 x 0.4 x x 1.76 = 1.267 T

of Passive

Earthfill = 0.5 x 1.0 x 1.8 x 1.8 x 1.76 = 2.851 T

4.118 T

Self weight to be accounted = 1 x 4.12 = 1.373 Tm

3

Summary of Loads considering Passive Pressure.

Loads due to Horizontal Force in Tonnes

1Loads excluding Passive Pressure

H = 58.88 V = 148.0

2Self weight of passive Earthfill

- W = 1.37

3 FH = -1.70 2.3

Total 57.17 151.58

Check for Sliding

x Cos (q + d )

x Cos (q + d )

HORIZONTAL FORCE(FH)

SFV SFH

Sr.No. Vertical Load in

Tonnes

Passive earth pressure component. FV =

SH = SV =



.25





m = 0.45 V = 151.6 T H = 57.17 T

Factor of Safety = 0.45 x 151.6 = 1.193 Hence Unsafe

57.17

Hence, provide shear Key.

It is necessary to provide a factor of safety of 1.5 against sliding

Hence,the wall should be safe for horizontal pressure = 1.5

= 1.5 x 57.17 = 85.759 T/m²

Available friction = m = 0.45 x 151.6 = 68.212

= 1.5 x -

= 1.5 x 57.17 - 0.45 x 151.6

= 17.547 T

Design of Shear Key : -

Design requirements as per IRS code of practice for plain reinforced and prestressed concrete

for general bridge construction 1982

196 N/mm² = Tension other than shear reinforcement

157 N/mm² = Permissible stress in tension for shear reinforcement.

Using M30 mix concrete

fc = 30 mix (controlled section)

= 0.34 x fc = 10.2 N/mm²

= 0.26 x fc = 7.8 N/mm²

= 0.034 x fc = 1.02 N/mm²

For M30 grade concrete

Design Constants

m = Modulur ratio = 276 = 276 = 9.020

3 x 10.2K = = 9.020 x 10.2 = 0.319

9.020 x 10.2 + 196

j = 1 - K = 1 - 0.319 = 0.8935

3 3

R = = 10.2 x 0.894 x 0.319 = 1.456

2 2

b = Length of the member considered = 1000 mm D = Total width of member

x SH

x SV

\ Unbalanced Force SH m x SV

sst =

sst =

Permissible stress in conc in bending scPermissible stress in direct compression scbc Permissible stress for shear sv

3scmscbc

msabc + sst

scbc.j.k



.26





d = Effective width of member

Safe bearing pressure for lateral loads may be taken as = 0.7 times safe bearing pressure for vertical loads.

Safe bearing pressure for Vertical Loads S.B.C = 25.00 T/m²

0.7 x S.B.C

= 17.50 T/m²

Safe Horizontal Pressure x y = Unbalanced Force

Unbalanced Force = 17.547 = 1002.7 Say 1010.0 mm

Safe Horizontal Pressure 17.50

1010.0 mm

Max. B.M = Unbalanced Force x y = 17.547 x 1.01 = 8.861 Tm

2 2

Check for effective width

d = B.M = 8.861 = 246.724 mm

Rb 1.456 1000

D = d + Cover +

= 246.7 + 75 + 6 = 327.724 Say 330.0 mm

330 - 75 - 6 = 249 mm

Area of Steel (At)

At = M = 196 N/mm²

j = 0.89

= 8.86 x d = 249 mm

196 x 0.89352 x 249

= 2032.04 mm²

At (minimum) = 0.2 x bD = 0.2 x 1000 x 330 = 660 mm²

100 100

Provide 20 mm Tor bar

Area of bar 20 mm Tor Steel = 314.00 mm²

Spacing = 314.00 x 1000 = 154.52 mm

2032.04

20 @ 150.00 mm c/c as main steel

DESIGN OF DOUBLY REINFORCED BEAM:

c = 10.2 N/mm² t = 196 N/mm² D = 300 mm

\ Safe Horizontal Pressure =

\ y =

\ Provide Key of height = y =

x 107

f/2

\ deff. =

sst

sst.j.d

107 '

\ Provide Tor

B995

user 4: Singly reinforced beam is hidden in cells 761 to 779. Whenever required unhide the same.



.27





m = 9.020 d = D - dc = 240.00 dc = 60 mm

MR = B.M = 8.861 N mm b = 1000 mm

Diameter of Compression Reinforcement = 20 mm

Diameter of Tension Reinforcement = 20 mm

1 Depth of Critical N . A

c = n

t m (d - n)

10.2 = n

196 9.02 (d - n)

10.2 x 9.02 x 240.0 - 10 x 9.02 n = 196.0 n

10.2 x 9.02 x 240.0 - 10.2 x 9.02 n = 196.0 n

22080 = 92.00 n + 196.0 n

22080 = 288.0 n

n = 76.6667 mm

2 Stress in Concrete at Level of Compression Steel

c' = n - dc

c n

c' = ( 76.7 - 60.0)

10.2 76.667

c' = 10.2 x 16.667

76.667

= 2.2174 N/mm²

3 MR = b n c / 2 ( d - n / 3 ) + ( m - 1 ) Ac . c' ( d - dc )

8.861 = 1000 x 76.667 x 10.2 240.0 - 76.7

2 3

+ ( 9.02 - 1) x Ac x 2.217 ( 240.0 - 60)

88611684 = 83847777.777778 + 3200.87 Ac

= 1488.316 mm²

Spacing for 20 mm diameter of bar

Area = 20² = 314.29 mm²

4

No. of Bars = Ac = 1488.3 = 4.736 mm

Area of one bar 314.29

Spacing = 1000 = 267.70 say 265 mm

3.736

Provide 20 mm dia bar @ 265 mm c/c as compression steel

4 Calculation of tensile steel

Total Compression = Total Tension

x 107

x 107

\ Ac

p x



.28





b x n x c + (m - 1) x Ac x c' = At x t

2

1000 x 76.667 x 10.2 + ( 9.02 - 1) x 1488.3 x 2.217

2

= At x 196

At x 196 = 417466.146

At = 417466.146 = 2129.9293 mm²

196

Spacing for 20 mm diameter of bar

Area = 20² = 314.29 mm²

4

No. of Bars = 2129.9 = 6.777

314.29

Spacing = 1000 = 173.10 say 170.0

5.777

Provide 20 mm dia bar @ 170 mm c/c as tensile steel

5 Distribution Steel

Distribution steel = 0.2 x bD = 0.2 x (1000 x 300 ) = 600 mm²

100 100

2/3 of above reinforcement provided on both the faces.

2 x 600 = 400.00 mm²

3

Provide 10 mm Tor bar

Spacing = 78.5 x 1000 = 196.250 mm Say 195 mm

400.000

10 Tor @ 195 mm c/c as distribution steel

Stresses for Wing Wall .:-

Sr. No. Section Considered Compression in T/m² Tension in T/m²

1 1.50 below F.L 5.850 0.000

2 At 2 nd Batter Level 94.610 -54.871

3 20.721 0.000

p x

\ Distribution Steel =

\ Provide

At top of bottom foundation concrete



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Foundation Pressure

Pmax. = 24.665

Pmin. = 18.211 SINCE Pmin +ve NO TENSION

Stability check

Factor of Safety against Overturning = 3.214

Factor of Safety against Sliding = 1.131 < 1.5 Hence, provide shear Key.

Details of shear key

Height of shear key = 1010 mm

Width of shear key = 300 mm

Main steel

Tensile Steel : Tor 20 mm @ 170 mm c /c

Compression Steel : Tor 20 mm @ 265 mm c /c

Distribution steel Tor 10 mm @ 195 mm c /c

T/m2

T/m2

Design of Wingwall at Chainage

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