design of wingwall at chainage
DESCRIPTION
wallTRANSCRIPT
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.6
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.
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
Total = 47.56 Total = 145
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.7
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.:
= 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
Total = 8.35 Total = 18
Section C' - C Moments about
C
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.8
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 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
Total = 40.66 Total = 202
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
Total = 53.21 Total = 299
Calculation of Earth Pressures on Wing Wall with Surcharge :
ZONE 1
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.9
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.:
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
* Required for Calculation of vertical and 0.275 ( 1 + 0.773)
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)
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 )
i3 = q3 = tan-1
f = d3 = K3 = Cos² (f - q)
2
2
2
2
2
2
2
2
2
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.10
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.:
= 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
* Required for Calculation of vertical and 0.979 ( 1 + 0.538)
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)
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 )
a = f = w = T/m2
T/m2
2
2
2
2
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.11
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.:
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.12
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.:
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)
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.13
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.:
=
= 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)
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.14
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.:
= 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'
P1a x Sin q1 + d1 P2a x Sin q1 + d1 P1a x Cos q1 + d1 P2a x Cos q1 + d1= 2.334 = 9.621 = 7.072 = 29.153
P1b x Sin q2 + d2 P2b x Sin q2 + d2 P1b x Cos q2 + d2 P2b x Cos q2 + d2= 4.900 = 17.279 = 3.223 = 11.365
D - D'
P1a x Sin q1 + d1 P2a x Sin q1 + d1 P1a x Cos q1 + d1 P2a x Cos q1 + d1= 2.798 = 9.621 = 8.480 = 29.153
P1b x Sin q2 + d2 P2b x Sin q2 + d2 P1b x Cos q2 + d2 P2b x Cos q2 + d2= 5.574 = 17.279 = 3.666 = 11.365
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)
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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.: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 BB
(S+V)surcharge on CC H1 =
(S+V)surcharge on DD
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.16
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.:
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:
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
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 BB
(S+V)surcharge on CC H1 =
(S+V)surcharge on DD
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.17
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.:
= 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
Batter at earthfill side 2
= 1.800 + 1.026 + 0.450 + ( 4.635 - 0.15 - 0.3 ) + 2.337
9 2
= 4.933 m
5) Moment = Total Load x Lever arm
= 3.657 x 4.933
= 18.039 T m
Section D - D:
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 = 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
Batter at earthfill side 2
= 0.400 + 1.800 + 1.026 + 0.450 + ( 4.635 - 0.15 - 0.33 ) + 2.737
9 2
= 5.533 m
5) Moment = Total Load x Lever arm
= 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)
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
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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.:
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.19
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.:
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
Sr. No. Loads and Moments due to
1 Self Weight of Wing Wall - 29.750 - 37.178
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
Total Vertical Load = 49.703 Tonnes
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
Total width at base of wing wall (w) = 2.502
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
Section Modulus = 1 x w² x L = 1 x 6.3 x 1.0 = 1.043 m³
6 6
Direct Stress = Total Vertical Load = 49.703 = 19.869 T/m²
Base Area 2.502
Horizontal Force (T)
Vertical Load
(T)
Overturning
(Tm)
Stabilising
(Tm)
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
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.20
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.:
Bending Moment @ at centre line of base of Wing Wall = Vertical load x eccentricity
= 49.703 x 1.568
= 77.950 Tm.
Bending Stress = Moment = ± 77.950 = ± 74.741 T/m²
Section Modulus 1.043
Resultant Stress = Direct Stress ± Bending Stress
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
Sr. No. Loads and Moments due to
1 Self Weight of Wing Wall - 47.558 - 145.057
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
7 Vertical Surcharge Load 3.657 18.039
Sum 50.81 126.0 147.9 533
Total Vertical Load = 126.010 Tonnes
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
Total width at base of wing wall (w) = 6.102
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
Section Modulus = 1 x w² x L = 1 x 37.2 x 1.0 = 6.205 m³
6 6
Horizontal Force (T)
Vertical Load
(T)
Overturning
(Tm)
Stabilising
(Tm)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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
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.21
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.:
Direct Stress = Total Vertical Load = 126.010 = 20.652 T/m²
Base Area 6.102
Bending Moment @ at centre line of base of Wing Wall = Vertical load x eccentricity
= 126.010 -x 0.003
= -0.426 Tm.
Bending Stress = Moment = ± 0.426 = ± 0.069 T/m²
Section Modulus 6.205
Resultant Stress = Direct Stress ± Bending Stress
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
Sr. No. Loads and Moments due to
1 Self Weight of Wing Wall - 53.908 - 185.991
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
Horizontal Force (T)
Vertical Load
(T)
Overturning (Tm)
Stabilising
(Tm)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)
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
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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.:
6
- 9.621 - 41.947
- 17.279 - 101.984
- 1.206 - 8.322
7 Vertical Surcharge Load 4.283 23.696
Sum 58.88 148.0 219.0 703.9
Total Vertical Load = 147.954 Tonnes
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
Total width at base of wing wall (w) = 6.902
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
Section Modulus = 1 x w² x L = 1 x 47.6 x 1.0 = 7.939 m³
6 6
Direct Stress = Total Vertical Load = 147.954 = 21.438 T/m²
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.
Bending Stress = Moment = ± 25.620 = ± 3.227 T/m²
Section Modulus 7.939
Resultant Stress = Direct Stress ± Bending Stress
(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:
Earth Pressure + Earthfill Surcharge (Vertical Force)
SH = SV = SO = SS =
SV =
SO - SS
SV
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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.:
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.24
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.:
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 =
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.25
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.:
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.26
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.:
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.27
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.:
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.28
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.:
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
S. N. BHOBE & ASSOCIATESARCHITECTS & CONSULTING ENGINEERS
62, MAHAVIR CENTRE, VASHI, NAVI MUMBAI 400 705
.29
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.:
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