Abutment Design
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Abutment Design
DESIGN OF ABUTMENT INPUT DATA Levels Proposed road level Existing ground level Depth of foundation Founding level Depth of superstructure Size of bearing Size of pedestal Number of bearings Bed block level Thickness of wearing coat C/C distance between face of dirt wall Projection of girder C/C distance between bearing
= = = = = = = = = = = = =
Dimensions Top width of abutment Bottom width of abutment Back batter Size of foundation Width of toe Width of heel Length of abutment
= = = = = = =
750 mm 900 mm 1 in 5600 x 3200 mm 1500 mm 8.20 m
Dirt wall thickness Dirt wall height Top width of Return wall Bottom width of Return wall
= = = =
400 0.825 0 0
Fly wing Depth of wing wall Thickness of wing wall
= = =
No 0.00 0.00
Concrete data and Permissible stresses Grade of concrete Grade of steel
= =
M 25 Fe 415
Unit weight of Concrete
=
25 kN/m3
Allowable Bending Stress (IRC:21-2000,Table - 9,Page18)
=
8.33 N/mm2
Allowable stress in Steel (IRC:21-2000,Table - 9,Page18) Modular ratio
=
200 N/mm2
100.773 94.823 900 93.623 600 400 700 5 99.948 75 6400 200 6000
=
10
mm mm x x
mm m m m
Unit weight of Soil
=
18 kN/m3
Angle of internal friction of soil
=
30
o
Surcharge angle Angle of inclination of wall from verticle face
=
0
o
=
88
Angle of friction between wall and soil
=
20
=
x x
36.166667 8200
x
50 100
mm mm mm mm
Soil data
Safe bearing capacity of soil
630 930
o
o
150 kN/m2
KLESCET Consultants
900
Abutment Design
Arrangement of Abutment System e2 300 3500 300
400
700
RL 100.773 Formation Level in Metre
Approach Slab
0
300 150
200 500
750 RL 99.948 Top of Abutment Cap in Metre
Abutment Cap
400
750
RL 99.548 Top of Abutment stem in Metre 350
375
998 750
6175
7150
5425
60 G.L
o
RL 94.823
0
RL 94.523 Top of Footing in Metre
A 1.20
0 900
1728
900
1500
150
750
RL 93.623 Foundation Level in Metre
3200
900 5600 SECTION OF ABUTMENT SYSTEM
Longitudinal eccentricity between CG of Bearing and CG of Abutment Stem
e1
=
0.225 m
Longitudinal eccentricity from centre of dirt wall to centre of pedestal Self Weight of Abutment Structure
e2
=
0.525 m
Element No.
Description of structure
1
Footing
2
3 4 5 6 7 8 9
Shape
Rectangle Triangle Rectangle Abutment Wall Rectangle Triangle Rectangle Triangle Abutment Cap Rectangle Dirt Wall Rectangle Approach slab Rectangle bracket Triangle Return Wall Rectangle Triangle Pedestal Rectangle Fly wing Rectangle Triangle Soil over burden Rectangle Triangle Triangle TOTAL C.G of abutment about A
Dead load from superstructure
Nos.
Length (m)
1 1 1 1 1 1 1 1 1 1 1 2 2 5 0 0 1 1 1
8.2 8.20 8.20 8.2 8.2 8.2 8.2 8.2 8.2 8.2 8.2 1.50 0.15 0.93 1.728 1.728 8.2 8.2 8.2
Lever Arm Bredth Depth (D) Area (m2) about (B) point A (m) 3.65 1.50 1.50 0.75 0.15 0.75 0.35 1.1 0.4 0.3 0.3 0.00 0.00 0.70 0.00 0.00 1.50 0.15 1.5
0.90 0.00 0.90 5.425 5.425 0.35 0.35 0.4 0.75 0.3 0.15 6.25 5.425 0.10 0.00 1.00 6.250 5.425 0
3.285 0 1.35 4.06875 0.406875 0.2625 0.0613 0.440 0.300 0.09 0.0225 18.75 0.81375 0.35 0.000 0.000
30.20 = = =
128.26 30.20 4.25 m 394.36 kN
KLESCET Consultants
3.650 4.600 4.850 3.575 4.000 3.575 4.067 3.750 4.100 4.450 4.400 4.850 4.050 3.700 6.464 6.176 4.850 4.050 5.10
Weight (kN)
Moment @ Toe of Footing (kN.m)
673.43 0.00 276.75 834.09 83.41 53.81 12.56 90.20 61.50 18.45 4.61 0.00 0.00 8.14 0.00 0.00 1383.75 83.41 0.00 3584.11
2458.001 0.000 1342.238 2981.885 333.637 192.380 51.062 338.250 252.150 82.103 20.295 0.000 0.000 30.109 0.000 0.000 6711.187 337.808 0.000 15131.10
Abutment Design
SUMMARY OF LOAD CALCULATION
CASE1: WORKING CONDITION
Moment due to Active Earth Pressure
Moment due to Live load Surcharge
=
133.51 x
=
400.942
kN.m/m
= =
44.816 160.217
x
7.15
0.5 kN.m/m
0.42
x
7.15
x
x
Total Moment due to soil & surcarge For 8.20 m carrigeway Total Moment due to soil & surcarge
=
561.16
=
4601.503
kN.m/m kN.m
CHECK FOR STABILITY (Refer IRC : 78 - 2000, Cl.No.706.3.4, Pg.No.21) Sl.No. DESCRIPTION VERTICAL HORIZONTA RESISTING OVERTURNI OF FORCES FORCE L FORCE (kN) MOMENT NG MOMENT (kN) (kN-m) (kN-m) 1 2 3 4
Dead load from superstructure Live Load from Superstructure Load from Abutment structure Active Earth Pressure & surcharge
394.36
-
1459.13
-
247.42
-
884.51
-
3584.11
-
15131.10
-
532.24
1462.30
-
4601.50
5
Braking force
-
123.71
-
1032.96
6
Secondary force
-
25.34
-
158.99
i) Construction stage a) F.O.S against Sliding
= = =
b) F.O.S against Overturning
= = = KLESCET Consultants
0.6 x W > H 0.51 4758.12 1611.35 1.51 SAFE
1.5
Mr Mo 15131.10 5793.46 2.61
2
>
Abutment Design
SAFE
KLESCET Consultants
Abutment Design
ii) Working condition a) F.O.S against Sliding
0.5*W > H 0.51 4758.12 1611.35 1.51 SAFE
= = =
b) F.O.S against Overturning
Mr Mo 17474.75 5793.46 3.02 SAFE
= = =
>
CASE 2 : SEISMIC CONDITION Moment @ bottom of Toe due to seismic due to soil
x
=
x
261.81
7.15
0.5
133.51
Moment @ bottom of Toe due to seismic and static due live load surcharge
Active earth pressure due to surcharge for static
=
617.78
=
16.52
=
77.94
=
0.20
= Total pressure
= =
Horizontal component
= = =
Moment @ bottom of Toe due to static
kN.m/m x
21.60
7.15
xx
0.309
7.15 x 9.54 kN/m
9.538 x 9.538 x 8.963 kN/m
=
8.96
cos 20 0.94
0.5 32.04 kN-m/m
=
77.94
32.04
45.90 kN-m/m
m carrigeway =
x
0.66 kN-m/m
x
1.334
= For 8.20 Total moment due soil and surcharge
2.38
1.334 kN/m2
= Moment @ bottom of Toe due to seismic
x
376.36 kN-m
KLESCET Consultants
7.15
1.5
2
Abutment Design
KLESCET Consultants
Abutment Design
CHECK FOR STABILITY (Refer IRC : 78 - 2000, Cl.No.706.3.4, Pg.No.21) Sl.No. DESCRIPTION VERTICAL HORIZONTA RESISTING OVERTURNI OF FORCES FORCE L FORCE (kN) MOMENT NG MOMENT (kN) (kN-m) (kN-m) 1 2 3 4
Dead load from superstructure Live Load from Superstructure Load from Abutment structure Load from soil pressure & surcharge
394.36
-
1409.84
-
49.48
-
884.51
-
3584.11
15131.10
385.09
1058.02
5442.12
-
85.18
615.44
5
Seismic force
6
Breaking force
123.71
1032.96
7
Secondary force
25.34
158.99
i) Construction stage a) F.O.S against Sliding
= = =
b) F.O.S against Overturning
= = =
0.5*W > H 0.5 3969.19 1292.25 1.54 SAFE Mr Mo 15131.10 7249.52 2.09 SAFE
>
1.25
1.5
ii) Working condition a) F.O.S against Sliding
= = =
b) F.O.S against Overturning
= = =
KLESCET Consultants
0.5*W > H 0.5 4413.04 1292.25 1.71 SAFE Mr Mo 17425.46 7249.52 2.40 SAFE
>
1.25
1.5
Abutment Design
CHECK FOR BASE PRESSURE
For working condition S.B.C. of soil Total load
W ML
x = Length of footing Total width of footing
ML/W L B B/6
Eccentricity
e
=
150
= = = = = = = =
4758.12 Mr - Mo 17474.75 11681.29 2.455 8.20 5.60 0.93
= =
B/2 - x 0.34 m
kN/m2 kN -
5793.46
kN.m m m m m
< (B/6)
SAFE
Pressure, Max Pressure at Base = = =
(W/BxL)x(1+(6e/B) 150.00/(8.20x5.60)x(1+6x0.34/5.60) 141.92
kN/m2
Min Pressure at Base = = Hence
= < S.B.C
Max Pressure
(W/BxL)x(1-(6e/B) 150.00/(8.20x5.60)x(1-6x0.34/5.60) 65.32
kN/m2 SAFE
For seismic condition S.B.C. of soil Total load
W ML
x = Length of footing Total width of footing
Eccentricity
ML/W L B B/6 e
=
225
= = = = = = = =
4509.31 Mr - Mo 17425.46 8661.55 1.921 8.20 5.60 0.93
= =
B/2 - x 0.88 m
kN/m2 kN -
8763.91
kN.m m m m m
< (B/6)
SAFE
Pressure, Max Pressure at Base = = =
(W/BxL)x(1+(6e/B) 150.00/(8.20x5.60)x(1+6x0.88/5.60) 190.70
kN/m2
Min Pressure at Base = = Hence
Max Pressure
= < S.B.C KLESCET Consultants
(W/BxL)x(1-(6e/B) 150.00/(8.20x5.60)x(1-6x0.88/5.60) 5.70
kN/m2 SAFE
Abutment Design
DESIGN OF RETURN WALL
0.30
FRL=
RL100.773
Due to surcharge
h= 6.25 m Top of footing = RL94.523
Soil parameters KA
= = = =
30 0 88 20
=
18
=
0.309
1). Active Earth Pressure Active Earth pressure, p=
Total Pressure=
0.5 h
0.42 h
1.2*Ka*
0.90 C/s of Return wall
Due to Soil
Ka**h
° ° ° ° kN/m3
= =
Ka 0.309 x
=
34.741 kN/m
= =
x
h 6.25
p x 34.741
h 6.25
2
0.5 0.5
x
= = =
108.565 kN/m 108.565 x cos x 20 102.017 kN/m
Vertical component=
= =
108.565 x sin x 20 37.131 kN/m
Moment @ bottom of Toe=
= =
lever arm h 102.017 x 0.42 x 6.25 267.796 kN.m/m
Horizontal component=
2). Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge = =
Active Pressure due to surcharge
Total Pressure
1.2 1.2
x Earth fill 18 x
=
21.600
= = =
Ka x 1.2 0.309 x 1.2 6.670 kN/m
=
6.670
kN/m2
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h
x x
18 18
Abutment Design
= =
6.670 6.25 41.689 kN/m
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Abutment Design
Horizontal component
= =
41.689 x cos 20 39.175 kN/m
Vertical component
= =
41.689 x sin 20 14.258 kN/m
= =
lever arm 39.175 0.5 x 122.421 kN.m/m
Moment @ bottom of Toe
x
6.25
Total Vertical Comp.Force due to soil & surcharge Total Horizontal comp.Force due to soil & surcharge Total Moment due to soil & surcharge Hight of Dpro at base of wall Therefore "d" available = 0.900 Grade of concrete Grade of Steel According to IRC-21:2000 Design Constants: σcbc Modular Ratio Neutral Axis Factor
= = = 6.250 m 900 mm
= =
25 415
=
8.33 N/mm2
σst m
= =
200 N/mm3 10
k
=
m σcbc/( mσcbc + σst)
= =
Lever Arm Factor
j
Q
=
1-(k/3)
dreq
=
1
8.333
-
+
200
0.294 3
0.90 0.5 x σcbc x j x k
=
0.5
=
1.11
=
x
10 x 8.333 0.29
= Moment Factor
10
=
=
51.390 kN/m 141.192 kN/m 390.217 kN.m/m
x
8.333
390.22 x 1000000 1.11 x 1000
KLESCET Consultants
x
0.90 x
0.29
Abutment Design
Dia of bar Overall Depth Provided Clear Cover Center of reinforcement Effective depth Provided
= = = = = =
594.2 32 900 50 16 834
mm mm mm mm mm mm
KLESCET Consultants
< dreq
SAFE
Abutment Design
Area of Steel Required
=
Area of Steel Required
Minimum reinforcement required
Hence required Diameter of bar
M x 106 j x σst x d
=
390.22 x 1000000 0.902 x 200 x 834.000
=
2593.71 mm2/m
= =
0.12 % of cross sectional area 0.12% x 900 x 1000
=
1080 mm2/m
Ast,req
>
Astmin
Ast
= =
Spacing required Spacing provided
= =
2593.71 mm2/m 32 mm 310.1 125
mm2
Provide 32mm dia bars @125mm C/C Total Steel Provided on Embankment Face
=
6433.98 mm2 SAFE
Check for Shear As per IRC-6:2000, Cl:304.7.1.1.1. Shear Force
V
=
141.192 kN
v
= = = =
141.192 x 1000 x 0.169295
Pt
=
(100 x Ast) / (B x d)
= = = As per IRC-6:2000, Table 12B, Page no 37.
100 x 6433.98 1000 x 834.00 0.771
Design Shear stress
Pt
1000 834
0.37 0.31
c =
0.375151
>
v
x
0.50 c
SAFE
0.771 0.271 0.25
KLESCET Consultants
0.06
0.75
Dirt Wall Design
DESIGN OF DIRT WALL Dirt wall is designed as a cantilever member subjected to following loads 1)Active earth pressure 2)Live load surcharge 3)Braking force 0.4
Live load surcharge
h=
Active earth pressure
0.825 m 0.5 h
0.42
1.2*Ka*
C/s of Dirt wall
h
Ka**h
Height of Dirt wall, h = FRL-Top of Abutment cap FRL= h
=
=
100.773 0.825
99.948 m
h =
Top of Abutment cap= Soil parameters = KA =
30 0 88 20
˚ ˚ ˚ ˚
18 kN/m3 0.309
1). Active Earth Pressure Active Earth pressure, p
Total Pressure
Horizontal component
=
Ka
=
0.309
=
4.586
kN/m2
=
0.5 x
=
0.5
x
p
1.892 kN/m
=
1.892 x cos 1.778
0.825
h
x
4.586
=
=
h
x
0.825
x
kN/m x
x
KLESCET Cosultants
20
100.773 m 0.825
99.948 m
Dirt Wall Design
Vertical component
= =
Moment @ bottom of Dirt wall
= =
1.892 x sin 0.647
x
20
kN/m
lever arm 1.778 x 0.42 x 0.616
0.825
kN.m/m
2). Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge = 1.2 x Earth fill =
ctive Pressure due to surcharge
Total Pressure
1.2 x
=
21.600
=
Ka
18 kN/m2 1.2
x
=
0.309 x
=
6.670
=
6.670 x
=
6.670 x 0.825
=
5.503
x
1.2 x kN/m2 h
kN/m
KLESCET Cosultants
18
Dirt Wall Design
Horizontal component
Vertical component
Moment @ bottom of Dirt wall
=
5.503
cos 20
=
5.171 kN/m
=
5.503
x
sin 20
x
=
1.882
kN/m
=
5.171 x
=
2.133
lever arm 0.5 x
0.825
kN.m/m
3). Braking Force Following Vehicles are considered to act on Dirt Wall a) 70R Bogie b) Class A ( Two Lane ) According to the IRC-21:2000, Cl:214.20, Page no 33, braking force is taken as 20% of actual load of wheel on the span a) 70R Bogie
H 1.2
85.00 2.13
Wheel Load
85.00 1.93
0.825
a= 2.025
In Plan 0.22 0.86
0.86 FOOTING
Minimum Axel width in longitudinal direct
1.37
Effective width of dispersion, beff 1.2a + b1 Braking force acts at 1.2 m above Road level Thickness of wearing coat = 75.0 mm b1 = 0.86 + 2 x 0.075
m (Refer Cl.305.16.2 of IRC:21- 2000) (Refer Cl.214.3 of IRC:6- 2000) =
1.010
m
1.2 x 2.025 + 1.010 = 3.440 beff > Spacing of the wheels (1.2m) hence dispersion width over laps
m
beff =
Total Dispersion Width
=
Tb
=
Total axel load
=
2.13
+ 1.93 + 3.440 /
2
5.780 m
Braking Force(20% of axel load), H Braking Force per metre width
170 kN = =
KLESCET Cosultants
34.0 H/Tb
kN
(Refer Cl.214.2 of IRC:6- 2000)
Dirt Wall Design
=
5.882
kN/m
b) CLASS A (2 No.) 57.0 0.9
Wheel Load
In Plan
57.0 1.8
57.0 1.7
0.25
57.0 1.8
0.25
0.5 Minimum Axel width in longitudinal direct
0.5 1.2
m
b1 =
0.5
+
x 0.075
=
0.650
m
beff =
1.2
x 2.025 + 0.650
=
3.080
m
2
KLESCET Cosultants
Dirt Wall Design
beff > Spacing of the wheels (1.2m) hence dispersion width over laps Total Dispersion Width = 0.5+0.15+0.25+1.8+1.7+1.8+(4.506/2) Tb = 7.740 m Total axel load = 228 kN Braking Force(20% of axel load) = 45.6 kN Braking Force per metre width = 5.891 kN/m Hence Class 'A' 2 Vehicle is critical, hence governs the design lever arm Moment due to Braking = 5.891 x 2.025 = 11.93 kN/m = =
Total Bending Moment
Design S.F
= =
Depth Required
11.93 + 0.616 + 0.616 + 15.295 kN.m/m (1.78+5.17+5.89) 12.840 kN
15.30 x 1000000 1.11 x 1000 117.6 mm
=
dreq
=
Overall Depth Provided Clear Cover Diameter of bar
= = =
400 50 20
mm mm mm
Center of reinforcement
=
10
mm
Effective depth Provided
=
340
mm
Area of Steel Required
0.20% x 400
= =
800.00
Spacing required
=
393
mm
Spacing provided
=
150
mm
Astreq
> dreq
15.30 x 1000000 0.902 x 200 x 340 j st. stress eff.depth 249.38 mm2/m
= =
Astmin
2.133
x
1000
mm2/m
< Ast min
Astreq =
800.000 mm2
Provide 20mm dia bars @150mm C/C Total Steel Provided on Embankment Face = KLESCET Cosultants
2094.40 mm2/m
Dirt Wall Design
SAFE
KLESCET Cosultants
Dirt Wall Design
Check for Shear (Refer IRC-6:2000, Cl.304.7.1.1.1, Shear Force
V
=
v
Design Shear stress
100Ast/(bd)
12.840 kN
=
12.840 x 1000 1000 x 340
=
0.038
=
100 x 2094.40 1000 340 x
=
0.616
N/mm2
0.31 0.23
0.25 As per IRC-6:2000, Table 12B, Page no 37. c = c
>
0.347 v
N/mm2
SAFE
KLESCET Cosultants
x
0.616 0.366 0.25
0.08
0.50
Abutment Design
LOADINGS 70-R Wheeled
170
170
170
1.37
3.05
170 1.37
0.2
120 2.13
120 1.52
80 3.96
6 1.17
RA
RB
RA
=
170 x 6.2 + 170 x 4.83 + 170 x 1.78 + 170 x 0.41 + 120 x -1.72 + 120 x -3.24 + 80x-7.2
=
179
kN
Class A 68
68
68
3
68
3
3
0.2
114 4.3
114 1.2
27
27
3.2
1.1
6 2.8
RA RA
RB =
68 x 6.2 + 68 x 3.2 + 68 x 0.2 + 68 x -2.8 + 114 x -7.1 + 114 x -8.3 + 27x-11.5 + 27 x
=
-324 kN
For two lane of Class A
=
-648.0 kN
350
+
350
=
50
50
50
50
50
50
50
0.653
0.653
0.653
0.653
0.653
0.653
0.653
Class 70 R Tracked Total load =
700 kN
KLESCET Consultants
Abutment Design
4.57 50
50 0.653
50 0.653
50 0.653
0.2 0.453 RA
RA
50 0.653
50 0.653
50 0.653
6 RB
=
50 x 6.2 + 50 x 5.55 + 50 x 5 + 50 x 4.24 + 50 x 3.59 + 50 x 2.94 + 50x2.28
=
247
kN
KLESCET Consultants
Abutment Design
Eccentricity in transverse direction Width of carriageway No of lanes
= =
8.20 m 3.00
1 lane of Class A
0.45 0.5
0.15
1.80 8.20
eT
= =
4.1 2.35 m
1.8
2 lanes of Class A
0.45
0.5
0.15
1.80
1.2
8.20
eT
= =
4.1 0.60 m
3.50
KLESCET Consultants
Abutment Design
3 lanes of Class A
0.45
0.5
1.2
0.15
1.80
1.2
1.80 8.20
eT
= =
4.1 1.15 m
5.25
KLESCET Consultants
1.80
Abutment Design
1 lane of Class 70 R
0.45
0.86
0.15
1.93 8.20
eT
= =
4.1 2.105 m
2.00
1 lane of Class 70 R + 1 lane of Class A
0.45
0.86
0.15
0.5
1.93
1.2
1.80 8.20
500
1.93
500
277
1.88
277
1.80
KLESCET Consultants
Abutment Design
Eccentricity due to load
eT
= =
=
4.1 0.770 m
2.30009
3.33
KLESCET Consultants
Abutment Design
DESIGN OF ABUTMENT WALL The abutment wall is designed as a section subjected to Axial force and Bending moment for the following forces 1) Self weight 2) Dead load from superstructure 3) Vehicular live load from superstructure e= 0.525 4) Braking forces 5) Horizontal forces due to secondary effects 6) Active Earth Pressure 400 700 7) Live load surcharge 300 750 0.8 FRL= RL100.773 Due to surcarge Due to Soil150 0.225 Abutment Cap
h=
6.25 m
400
750 0.5 h
Topof foot RL94.523
1.2*Ka*
99.548
0.42 h Ka**h
5.025 750 94.523
Soil parameters = = = = = Ka = Ca =
1). Self weight 1)Dirt wall
Moment @bottom of Wall 2)Abutment cap Rectangular area Moment @bottom of Wall Triangular Area Moment @bottom of Wall
3)Wall
C/L of wall 30 0 88.4161884 20 18 0.309 0.569
˚ ˚ ˚ ˚ kN/m3
= =
0.4x0.75x1x25 7.5
= =
7.5
= = = = = = =
1.1x0.4x1x25 11 kN/m 11 0.175 x 1.925 0.5x0.35x0.35x1x25 1.53125 1.53125 x 0.491666667 0.752864583
= =
0.75x5.02x1x25 94.21875 kN/m
x
3.94
kN/m
lever arm 0.525 kNm/m
KLESCET Consultants
Abutment Design
2). Dead load from super structure Total, R Load per meter width Wd Long. Moment ( ML )
394.36 = = = = =
(from staad analysis) R 8.20 48.09 kN/m lever arm x Wd e1 48.09 x 0.225 10.82 kNm/m
3). Vehicular live load from super structure Following Vehicular loads are considered Eccentricity, e1= 0.225 m
R/meter Moment Total Type of Load Reaction Rm ML=Rm*e1 in kN R A) Class A( 2 No-647.97 -79.02 -17.78 B) Class A( 3 No-971.95 -118.53 -26.67 C) 70R Tracke 494.83 60.35 13.58 D) 70R -3.97 Wheeled + -144.62 -17.64 Class A (1 No.) D) 70R 4.69 tracked + 170.85 20.84 Class A (1 No.) Hence 70R Wheeled + Class A Vehicle governs the design
Long. Moment ML = Total , R=
13.58 494.83
eT
Resultant
2.35 0.60 2.11 1.15
554 1108 1000 1662
kNm/m kN
Moment Type of Load A) Class A( 1 No B) Class A( 2 No C) 70R Wheele D) Class A( 3 No
E) Class A( 1 0.77 No.) + 70R Wheeled Total transverse moment Total transverse moment/m
1554 = =
MT=Rm*eT 1301.90 664.80 2105.00 1911.30 1196.44 2105.00 kNm 256.71 kNm/m
4). Braking forces (20 % of Axle Load upto 2 Lane & 5 % live load for additional lane.) As IRC-6:2010, horizontal seismic forces in the direction perpendicular to the traffi 20.00 % Total Axial load(kN) 1st 2nd lane
3rd Lane
For Static
5.00% -32.40 -48.60
Force -161.99 -242.99
Type of Load 1) Class A 2 VEH 2) Class A 3 VEH
2 lane -647.97 -971.95
3 lane -647.97 -971.95
20.00% -129.59 -194.39
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(without impact)
Total in Force/A BM at kN bt /m Fdl -161.99 -19.76 -242.99 -29.63
-164.95 -247.43
Abutment Design
3) 70R tracked + Class (1 No.) 4) 70R A Tracked
170.85
170.85
34.17
8.54
42.71
42.71
5.21
43.49
494.83
494.83
98.97
24.74
123.71
123.71
15.09
125.97
-28.92
-7.23
-36.15
5) Class A( 1 -144.62 -145 No.) + 70R Wheeled Effective width of dispersion, 1.2*a+b1 1 for Class A = 0.41 beff= 70R Tracked = 1.00 beff= 70R Wheeled = 1.02 beff=
10.43 11.02 11.04
8.20
KLESCET Consultants
-36.15417 -4.40904 -36.82
Hence bef
Max =
125.97
=
8.20
m
Abutment Design
m Total width of dispersion = 8.20 kN total force/trestle= 24.74 ng. Moment due to braking = 125.97 kNm/m
lever arm for the Braking force(m)=
8.35
lever arm for the secondary forces(m)= 6.275
5). Horizontal forces due to secondary forces Span length Length of Bearing L Width of Bearing B Total depth of Bearing D No. of Steel laminates Thickness of steel laminate Shear Modulus G Modulus of elasticity of concr E Co efficient of thermal expans (IRC 6-2010, Cl 218.4, Page 46) Maximum Temperature (IRC 6-2010, Fig 8, Page 42) Minimum Temperature (IRC 6-2010, Fig 9, Page 43) Temperatue difference t
= = = = = = = = =
6000 630 400 50 4 3 1 25000.0 1.17E-05
mm mm mm mm
Strain due to Temperature
=
Deformation due to Temperature
= = =
Shear deformation
= =
Deformation / Depth 0.16
Force on each bearing
= = =
Shear deformation x Shear modulus
mm N/mm2 N/mm2 / oC
=
37.5 oC
=
10 oC
=
27.5 oC
Number of bearings Force on abutment Force / meter length along abutment
= = =
Moment @bottom of Wall
= =
0.00032 Strain x 0.00032 x 1.93 mm
5067.56 N 5.1 kN 5 25.34 kN 3.09 kN/m 3.09
x 6.275 19.39 kN-m/m
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Span 6000
x Area of bearing
Abutment Design
6). Active Earth Pressure Active Earth pressure, p
18 kN/m2
= = =
Ka 0.309 34.741
Total Pressure
= = =
0.5 p x 0.5 34.741 108.565 kN/m
Horizontal component
= =
Vertical component
= =
108.565 37.131
ment @ bottom of Abutment
= =
lever arm 102.017 0.42 6.25 267.80 kN.m/m
= = = = =
1.2 1.2 21.600 Ka 6.670
Earth fill 18 x kN/m2 1.2 x xx kN/m2
= = = = = = =
6.670 6.670 41.689 41.689 39.175 41.689 14.258
x
= =
39.175 122.421
=
274.08
=
566.59
7). Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge
Active Pressure due to
Total Pressure
Horizontal component Vertical component
Moment @ bottom of Abutment
Total Vertical Force, P Total Longitudinal Moment ML
h 6.25
h 6.25
108.565 cos 20 102.017 kN/m sin kN/m
x
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h 6.25 kN/m cos x kN/m sin kN/m
20
18
x
20 20
lever arm 0.5 6.25 kN.m/m
kN/m kNm/m
Abutment Design
DESIGN OF ABUTMENT AS WALL Longitudinal moment
ML
Effective depth required
=
dreqd.
Overall depth provided Clear Cover Diameter of bar Half dia. of Bar Effective depth provided Area of Steel Required
Ast Spacing required Spacing provided
=
566.59 kNm/m
√(M /Q.b)
=
566.59 x 1000000 1.11 x 1000
= = = = = =
715.96 825.00 75.00 25 12.50 737.50
=
566.59 x 1000000 0.902 x 200 x
=
4258.8
= =
mm mm mm mm mm mm
> dreq SAFE 737.50
mm2
115 100 mm
Provide 25mm dia bars @100mm C/C Total Steel Provided
=
4908.74 mm2/m
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SAFE
Abutment Design
Check for Shear (Refer IRC-6:2000, Cl.304.7.1.1.1, Shear Force
V
v
Design Shear stress
100Ast/(bd)
=
141.192 kN/m
=
141.192 x 1000 1000 x 738
=
0.19
N/mm2
=
100 1000
x 4908.74 x 737.5
=
0.666
0.42 0.37
0.75 As per IRC-6:2000, Table 12B, Page no 37. c
=
c
>
0.353 v
N/mm2 SAFE
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x
0.666 -0.084 0.25
0.05
1.00
Abutment Design
CALCULATION OF ACTIVE EARTH PRESSURE
i) Static case Active earth pressure is calculated using Columb's theory as per IRC:78 - 2000, Cl.710.1.3
Soil parameters
Unit weight of soil Angle of internal friction of soil Surcharge angle Angle of inclination of wall from horizontal face Angle of friction between wall and soil
= = = = =
18 30 0 88 20
kN/m3 ° ° ° °
F.L Due to surcarge
RL 100.773
Due to Soil
7.15 m
h=
0.5 h
0.42 h
Found. Lvl 1.2 x Ka x
RL 93.623
Ka x x h
Static Earth Pressure Diagram Active earth pressure coefficient Ka
=
sin 2 (- ) sin 2 x
sin ( - )
1
= 0.930
x
1
+
0.309
Active Earth Pressure = = =
Ka x 0.309 x 39.743 kN/m2
PA
= = =
0.5 p x x 0.5 x 39.743 x 142.08 kN/m
Horizontal component
= = =
Vertical component
= =
Active Earth pressure
Total Static Pressure
p
sin ( + ) sin ( - ) sin ( - ) sin ( + )
2
0.7735451475 0.99923607x
=
+
x x
PA
cos 20 x 142.083 x 0.94 133.514 kN/m PA
x
142.083 x
sin 20 0.34
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h 7.15
h 7.15
0.766 x
0.5
0.930 x
1.000
2
Abutment Design
x
=
48.595
kN/m
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Abutment Design
Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge = = = Active Pressure due to surcharge Total Pressure
Horizontal component
Vertical component
1.2 x Earth fill 1.2 x 18 21.600 kN/m2
= = = = =
Ka 1.2 x x 6.670 kN/m 6.670 h x 6.670 x 7.15 47.692 kN/m
= = =
47.692 47.692 44.816
cos 20 0.94 kN/m
= = =
47.692 sin 20 x 47.692 x 0.34 16.312xkN/m
x x
Total Vertical Comp.Force due to active earth pressure & live load surcharge Total Horizontal comp.Force due to active earth pressure & live load surcharge For
8.20
18
=
64.907
kN/m
=
178.330 kN/m
=
532.235 kN
=
1462.304 kN
m carrigeway
Total Vertical Comp.Force due to active earth pressure & live load surcharge Total Horizontal comp.Force due to soil & surcharge
ii) Seismic case Seismic active earth pressure coefficient Ca
=
( 1 + Av ) cos2 ( - - )
x
cos cos cos ( + + ) 2
1
+
1 sin ( + ) sin (- - ) cos ( - ) cos ( + + )
Where,
Ca
= =
13.6
=
1.036 0.794
=
Total AEP due to Static and Siesmic
tan-1(Ah/1-Av)
PAE
°
x
1
1 + 0.766 x 0.999618
0.569
=
0.5 x x h2 x Ca
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2
0.282 0.817
2
Abutment Design
= =
0.5x18x7.150x7.150x0.569 261.8 kN/m
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Abutment Design
F.L RL 100.773
Due to surcarge
Due to Soil
7.15 m
h=
0.66 h
0.5 h
Found. Lvl 0.2 x 1.2 x x Ca
RL 93.623
(Ca - Ka) x x h
Seismic Earth Pressure Diagram
Active Earth pressure
Total Seismic Pressure
p
PAEQ
Horizontal component
Vertical component
= =
(Ca - Ka) x 0.260 x
=
33.491
=
0.5
x
h 7.15
x
h
x
kN/m2
p
x
= =
0.5 x 33.491 x 119.73 kN/m
= = =
PAEQ
x
PAEQ
x
= = =
Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge q = =
7.15
cos 20 119.731 x 0.94 112.511 kN/m sin 20
119.731 x 0.34 40.950 kN/m
0.2 0.2
=
4.320
=
Ca
1.2 1.2
x x
x Earth fill
18
x
kN/m
2
(Refer IRC:6- 2010, Table 1, Pg.No.6) Active Earth pressure due to surcharge
p
= = Horizontal component
Vertical component
q
x
h
x
0.569 x x 17.58 kN/m
7.15
= = =
17.58 17.58 16.52
= = =
17.58 sin 20 x 17.58 x 0.34 6.01xkN/m
Total Vertical Comp.Force due to active earth pressure & live load surcharge
cos 20 0.94 x kN/m x
=
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46.962
kN/m
Abutment Design
Total Horizontal comp.Force due to active earth pressure & live load surcharge For
8.20
=
129.027 kN/m
=
385.088 kN
=
1058.020 kN
m carrigeway
Total Vertical Comp.Force due to active earth pressure & live load surcharge Total Horizontal comp.Force due to active earth pressure & live load surcharge
KLESCET Consultants
Abutment Design
DESIGN OF ABUTMENT STEM The length of column (Height) The following details obtained from Abutment Stem Design: (Nd) Load
=
6250mm
=
274.08kN
Moment
(Md)
=
566.59kN
Stem thickness
(h)
=
900mm
Breadth
(b)
=
1000mm
Grade of concrete
=
M25
Grade of steel
=
Fe415
Tension face reinforcement
=
20
Area of
20 mm dia. bars
Compression face reinforcement
@
=
180 c/c 314sq.mm
=
12
No. of bars in tension face
=
11.11
[or]
12
No. of bars in comp. face Area of steel in tension face ( AS )
=
5.56
[or]
6
=
3770sq.mm
Area of steel in comp. face ( A'S )
=
679sq.mm
Area of
@
12 mm dia. bars
e
Modular ratio
180 c/c 113sq.mm
=
10
As per page 365 of Reynold's Handbook To find eccentricity, Md e = Nd h 6 h 2 3h 2 Therefore,
e
=
566.59
x 274.08 900
=
6 900
= = >
1000
2 3
x
900
2 h/2
>
=
2067.2mm
=
150.0mm
=
450.0mm
=
1350.0mm
3h/2
Effective cover to tensile steel
=
Effective depth
=
50
+
20
=
60mm
=
840mm
2 900 - 60 fcu x h = 900
d = 840 60 b=
Assumed depth of N.A
1000 =
243.00mm
SAFE
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0%
Abutment Design
K1
= b.x
=
1,000 x 243
=
243000sq.mm
To determine the centroid of stressed area K1.x + e.As.d + (e-1) A's.d' 1/2 x = K1 + e.As + (e-1)A's 0.50x243,000x243 + 10x3,770x840 + (10x1.5-1)x679x60
=
1
=
2
=
3
=
= 212.83mm
243,000 + 10x3,770 +1.5x(10-1)x679
e-x
+
d
x
1-
2d
1
x
1-
d'
243
1-
2x840
=
x
+
840
=
3d
(e - 1)
2,067.25 - 212.83
=
(10x1.5-1) x
1-
243 3x840 60 243
Compressive stress in concrete Nd.1 Fcs
=
2.b.d + 3.A's.
1-
274.08 =
x
d'
1000
0.131x1,000x840 + 10.543x679x
d x
3.208 1-
60 840
= 7.551Mpa
FC
=
=
=
Nd bx+eAs+(e-1)A'S 274.08x 1000 1000x243+10x3,769.91+(10-1)678.58 274077.95 286806.37
= 0.956Mpa Fcs max
=
( Fcs + FC )
=
7.55
+
0.96
=
8.51MPa
>
8.33Mpa
UNSAFE
KLESCET Consultants
1
= 3.208
= 0.131
= 10.543
Abutment Design
Calculation of Tensile stress in steel Permissible tensile stress in steel = fcs (0.5 K1 + b3 A's) - Nd fst = As =
200.00Mpa
7.551x (0.5x243,000 + 10.543x679) - 274
1000
3769.9111843078
= 184.992Mpa fst max = ( fst + Fc ) 184.99
=
= 184.04MPa
-
0.96
<
200.00Mpa
SAFE Check for the depth of Neutral Axis: Actual depth of Neutral Axis based on the stress level in concrete and steel and the effective depth is calculated from the formula d xa
=
1+
840 fst
=
e.fcs
% error is assumed N.A
=
184.99
1+
=
243.49mm
10x7.55 243.49 - 243.00
x
243.49
100
=
0.20%
<
5 %
SAFE
CHECK FOR MINIMUM REINFORCEMANT IN THE SECTION : The length of column Min. radius of gyration
r
Effective length factor
=
6250.0mm
=
sqrt(I/A)
=
sqrt[(1,000x900^3) / (12x900x1,000)]
=
259.8mm
=
1.75
(Refer IRC:21-2000, Cl.306.1, Table 13) leff
Effective length
= leff/r =
Slenderness ratio,
Min. steel in pedestal
1.75 x 6,250
=
42.10
=
0.30%
(Refer IRC:21-2000, Cl.306.2.2, Pg.No.59)
20 f
Actual area of steel provided
180 c/c +
10937.5mm SHORT COLUMN
of gross area
0.30 x 1,000 x 900 =
(Ast + Asc)(
=
10,937.50 / 259.81
12 f
2700sq.mm
180 c/c )
= 3769.91118431 >
=
100
+
678.58401 =
2700sq.mm
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SAFE
4448sq.mm
Abutment Design
SEISMIC COEFFICIENT Seismic coefficient is calculated as per provisions made in IRC 6 - 2010, IS 1893 - 1984 and IITK guidelines. Soil type = Medium soil Zone number = V Zone factor Z = 0.36 (Refer IRC 6 -2010, Table 6, Pg.No.47) Importance factor I = 1.20 (Refer IRC 6 -2010, Table 7, Pg.No.51) Reduction factor R = 2.50 (Refer IRC 6 -2010, Table 8, Pg.No.52) CALCULATION OF TIME PERIOD (Refer IRC 6 -2000, Appendix - 2, Pg.No.61) T = 2√D/(1000F) Where, T = Fundamental period of the pier/abutment in secs for horizontal vibrations D = Appropriate dead load of the superstructure and live load in kN Horizontal force in kN required to be applied at the centre of mass of superstructure for one mm deflection at the top of the pier/abutment F = along the considered direction of horizontal force. = = = = =
Grade of concrete Dead Load Live load Self Weight of Abutment Total ( w )
25 394.36 494.83 983.87 1873.07
kN kN kN kN
Height of abutment
L
=
5425 mm
Breadth of abutment
B
=
8200 mm
Thickness of abutment wall
t
=
750 mm
Young's Modulus
E
=
5000√Fck
=
25000
=
(B x t3 / 12)
Moment of inertia
Igr
=
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N/mm2
8200 x 4.22E+08 12
Abutment Design
= T=2√W/(1000F) FL3 / 3EI F
=
1
=
3EI/L3
=
T
3
x25000.00 x2.88E+11
1.60E+011
=
135.418635 kN
=
0.235 Sec
Sa /g = 2.50 ( Refer IRC:6-2010, Cl.219.5.1, Pg.No.50) Design horizontal seismic coefficient Z I Sa Ah = 2Rg = =
(0.36x1.2x2.5) 2x2.5 0.216
Av is taken as (1/2)Ah as per IS: 1893: 1984 Av
=
0.108
KLESCET Consultants
2.88E+11 mm4
Abutment Design
For
8.20 m carrigeway
Seismic force at bearing level
=
0.216 x 394.36
= Longitudinal moment upto footing top level
=
85.18 kN
85.18
=
Longitudinal moment upto footing bottom level
=
x
6.325
538.77 kN-m
85.18
=
x
7.225
615.44 kN-m
Per running meter carriage way Seismic force at bearing level
=
10.39 kN/m
Longitudinal moment upto footing top level
=
65.70 kN/m
Longitudinal moment upto footing bottom level
=
75.05 kN/m
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Abutment Design
DESIGN OF FOOTING Abutment hight above footing Unit weight of soil Unit weight of concrete
= = =
B
1.5
6.3 m 18.0 kN/m3 25.0 kN/m3
1.0
3.2
A 0.9
0.9
0.9 5.6 65.319 kN/m2
141.916 kN/m2 85.836 kN/m2 99.514 kN/m2 Upward pressure diagram 112.5 kN/ 11.655kN/
m
22.5 kN/
mm
22.5 kN/
mm
m
Downward pressure diagram
Design of toe slab Outstand w.r.t face of Column Design Bending Moment at face of support
dreqd.
Overall depth provided Clear Cover Diameter of bar Half dia. of Bar Effective depth provided
= =
3.2 m 144.73 + 509.51 triangle rectangle
=
539.05
=
√(M /Q.b)
115.20 rectangle
kN-m/m
=
539.05 x 1000000 1.11 x 1000
= = = = = =
698.34 900.00 75.00 25 12.50 812.50
=
539.05 x 0.902 x
=
3677.8
mm mm mm mm mm mm
> dreq
SAFE Are of Steel Required
Ast Spacing required Spacing provided
= =
1000000 200 x
812.50
mm2
133 120 mm
Provide 25mm dia bars @120mm C/C Total Steel Provided =
4090.62
mm2/m
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SAFE
Abutment Design
Check for shear stress Shear is critical @ distance 'd' from face of support Centre line of abutment critcal section 0.8125
2.3875
99.51
m
141.916
kN/m2
kN/m
2
110.280 kN/m2 3.2 Shear Force across the critical section
V
=
37.77
+
triangle
Developed Shear Stress
=
247.34
=
V bd
= = 100 As
=
bd
53.72
rectangle
rectangle
kN/m
247.34 x 1000 1000 x 812.50 0.30
N/mm2
4090.62 xx 1000 x
x
=
263.3
0.50
100 812.50
%
Permissible Shear Stress (Refer IRC:21 -2000,Cl.304.7.1.3.3, Table 12B, Pg.No. 37) For 100 As/bd 0.50 0.75 Allowable Shear Stress, c=
0.311
MPa
c (Mpa) 0.31 0.37
>
SAFE
Design of heel slab Outstand w.r.t face of Column Design Bending Moment at the face of support
=
=
1.5
126.56 +
m
13.11
+
8.74 7.69
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73.48
Abutment Design
=
67.24
=
√(M /Q.b)
=
67.24 1.11
=
246.64
Overall depth provided Clear Cover Diameter of bar Half dia. of Bar Effective depth provided
= = = = =
900.00 75.00
Are of Steel Required
=
67.24 0.902 j
Ast
=
456.22
Ast(min)
=
0.12%
=
1080
mm2/m
=
1080
mm2/m
dreqd.
Ast,required Spacing required Spacing provided
kN-m/m
x 1000000 1000 x
mm
mm mm 16 mm 8.00 mm 817.00 mm
= =
> dreq
SAFE
1000000 817 x 200 xx st. stress eff depth
x
mm2/m 900
x
< Ast(min) x
1000
186 150 mm
Provide 16mm dia bars @150mm C/C Total Steel Provided Ast,provided
=
1340.41
SAFE
mm2/m
Check for shear stress Shear is critical @ face of support critical section 1.5
65.32
kN/m2 85.8
kN/m2
1.5 Shear Force across the critical section
V
=
168.75
=
89.13
+ 33.75 kN/m
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113.37
Abutment Design
Developed Shear Stress
=
V bd
=
89.13 1000
=
0.11
1000 817
x x
N/mm2
(As per IRC: 21-2000, Table 12A) 100 As
=
bd
=
1340.41 x 1000 x 0.164
100 817
x
%
Permissible Shear Stress (Refer IRC:21 -2000,Cl.304.7.1.3.3, Table 12B, Pg.No. 37) For 100 As/bd
Allowable Shear Stress, c=
0.204
c (Mpa)
0.15
0.20
0.25
0.23
MPa
>
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SAFE
DESIGN OF ABUTMENT INPUT DATA Levels Proposed road level Existing ground level Depth of foundation Founding level Depth of superstructure Size of bearing Size of pedestal Number of bearings Bed block level Thickness of wearing coat C/C distance between face of dirt wall Projection of girder C/C distance between bearing
= = = = = = = = = = = = =
Dimensions Top width of abutment Bottom width of abutment Back batter Size of foundation Width of toe Width of heel Length of abutment
= = = = = = =
750 mm 900 mm 1 in 5600 x 3200 mm 1500 mm 8.20 m
Dirt wall thickness Dirt wall height Top width of Return wall Bottom width of Return wall
= = = =
400 0.825 0 0
Fly wing Depth of wing wall Thickness of wing wall
= = =
No 0.00 0.00
Concrete data and Permissible stresses Grade of concrete Grade of steel
= =
M 25 Fe 415
Unit weight of Concrete
=
25 kN/m3
Allowable Bending Stress (IRC:21-2000,Table - 9,Page18)
=
8.33 N/mm2
Allowable stress in Steel (IRC:21-2000,Table - 9,Page18) Modular ratio
=
200 N/mm2
100.773 94.823 900 93.623 600 400 700 5 99.948 75 6400 200 6000
=
10
mm mm x x
mm m m m
Unit weight of Soil
=
18 kN/m3
Angle of internal friction of soil
=
30
o
Surcharge angle Angle of inclination of wall from verticle face
=
0
o
=
88
Angle of friction between wall and soil
=
20
=
x x
36.166667 8200
x
50 100
mm mm mm mm
Soil data
Safe bearing capacity of soil
630 930
o
o
150 kN/m2
KLESCET Consultants
900
Abutment Design
Arrangement of Abutment System e2 300 3500 300
400
700
RL 100.773 Formation Level in Metre
Approach Slab
0
300 150
200 500
750 RL 99.948 Top of Abutment Cap in Metre
Abutment Cap
400
750
RL 99.548 Top of Abutment stem in Metre 350
375
998 750
6175
7150
5425
60 G.L
o
RL 94.823
0
RL 94.523 Top of Footing in Metre
A 1.20
0 900
1728
900
1500
150
750
RL 93.623 Foundation Level in Metre
3200
900 5600 SECTION OF ABUTMENT SYSTEM
Longitudinal eccentricity between CG of Bearing and CG of Abutment Stem
e1
=
0.225 m
Longitudinal eccentricity from centre of dirt wall to centre of pedestal Self Weight of Abutment Structure
e2
=
0.525 m
Element No.
Description of structure
1
Footing
2
3 4 5 6 7 8 9
Shape
Rectangle Triangle Rectangle Abutment Wall Rectangle Triangle Rectangle Triangle Abutment Cap Rectangle Dirt Wall Rectangle Approach slab Rectangle bracket Triangle Return Wall Rectangle Triangle Pedestal Rectangle Fly wing Rectangle Triangle Soil over burden Rectangle Triangle Triangle TOTAL C.G of abutment about A
Dead load from superstructure
Nos.
Length (m)
1 1 1 1 1 1 1 1 1 1 1 2 2 5 0 0 1 1 1
8.2 8.20 8.20 8.2 8.2 8.2 8.2 8.2 8.2 8.2 8.2 1.50 0.15 0.93 1.728 1.728 8.2 8.2 8.2
Lever Arm Bredth Depth (D) Area (m2) about (B) point A (m) 3.65 1.50 1.50 0.75 0.15 0.75 0.35 1.1 0.4 0.3 0.3 0.00 0.00 0.70 0.00 0.00 1.50 0.15 1.5
0.90 0.00 0.90 5.425 5.425 0.35 0.35 0.4 0.75 0.3 0.15 6.25 5.425 0.10 0.00 1.00 6.250 5.425 0
3.285 0 1.35 4.06875 0.406875 0.2625 0.0613 0.440 0.300 0.09 0.0225 18.75 0.81375 0.35 0.000 0.000
30.20 = = =
128.26 30.20 4.25 m 394.36 kN
KLESCET Consultants
3.650 4.600 4.850 3.575 4.000 3.575 4.067 3.750 4.100 4.450 4.400 4.850 4.050 3.700 6.464 6.176 4.850 4.050 5.10
Weight (kN)
Moment @ Toe of Footing (kN.m)
673.43 0.00 276.75 834.09 83.41 53.81 12.56 90.20 61.50 18.45 4.61 0.00 0.00 8.14 0.00 0.00 1383.75 83.41 0.00 3584.11
2458.001 0.000 1342.238 2981.885 333.637 192.380 51.062 338.250 252.150 82.103 20.295 0.000 0.000 30.109 0.000 0.000 6711.187 337.808 0.000 15131.10
Abutment Design
SUMMARY OF LOAD CALCULATION
CASE1: WORKING CONDITION
Moment due to Active Earth Pressure
Moment due to Live load Surcharge
=
133.51 x
=
400.942
kN.m/m
= =
44.816 160.217
x
7.15
0.5 kN.m/m
0.42
x
7.15
x
x
Total Moment due to soil & surcarge For 8.20 m carrigeway Total Moment due to soil & surcarge
=
561.16
=
4601.503
kN.m/m kN.m
CHECK FOR STABILITY (Refer IRC : 78 - 2000, Cl.No.706.3.4, Pg.No.21) Sl.No. DESCRIPTION VERTICAL HORIZONTA RESISTING OVERTURNI OF FORCES FORCE L FORCE (kN) MOMENT NG MOMENT (kN) (kN-m) (kN-m) 1 2 3 4
Dead load from superstructure Live Load from Superstructure Load from Abutment structure Active Earth Pressure & surcharge
394.36
-
1459.13
-
247.42
-
884.51
-
3584.11
-
15131.10
-
532.24
1462.30
-
4601.50
5
Braking force
-
123.71
-
1032.96
6
Secondary force
-
25.34
-
158.99
i) Construction stage a) F.O.S against Sliding
= = =
b) F.O.S against Overturning
= = = KLESCET Consultants
0.6 x W > H 0.51 4758.12 1611.35 1.51 SAFE
1.5
Mr Mo 15131.10 5793.46 2.61
2
>
Abutment Design
SAFE
KLESCET Consultants
Abutment Design
ii) Working condition a) F.O.S against Sliding
0.5*W > H 0.51 4758.12 1611.35 1.51 SAFE
= = =
b) F.O.S against Overturning
Mr Mo 17474.75 5793.46 3.02 SAFE
= = =
>
CASE 2 : SEISMIC CONDITION Moment @ bottom of Toe due to seismic due to soil
x
=
x
261.81
7.15
0.5
133.51
Moment @ bottom of Toe due to seismic and static due live load surcharge
Active earth pressure due to surcharge for static
=
617.78
=
16.52
=
77.94
=
0.20
= Total pressure
= =
Horizontal component
= = =
Moment @ bottom of Toe due to static
kN.m/m x
21.60
7.15
xx
0.309
7.15 x 9.54 kN/m
9.538 x 9.538 x 8.963 kN/m
=
8.96
cos 20 0.94
0.5 32.04 kN-m/m
=
77.94
32.04
45.90 kN-m/m
m carrigeway =
x
0.66 kN-m/m
x
1.334
= For 8.20 Total moment due soil and surcharge
2.38
1.334 kN/m2
= Moment @ bottom of Toe due to seismic
x
376.36 kN-m
KLESCET Consultants
7.15
1.5
2
Abutment Design
KLESCET Consultants
Abutment Design
CHECK FOR STABILITY (Refer IRC : 78 - 2000, Cl.No.706.3.4, Pg.No.21) Sl.No. DESCRIPTION VERTICAL HORIZONTA RESISTING OVERTURNI OF FORCES FORCE L FORCE (kN) MOMENT NG MOMENT (kN) (kN-m) (kN-m) 1 2 3 4
Dead load from superstructure Live Load from Superstructure Load from Abutment structure Load from soil pressure & surcharge
394.36
-
1409.84
-
49.48
-
884.51
-
3584.11
15131.10
385.09
1058.02
5442.12
-
85.18
615.44
5
Seismic force
6
Breaking force
123.71
1032.96
7
Secondary force
25.34
158.99
i) Construction stage a) F.O.S against Sliding
= = =
b) F.O.S against Overturning
= = =
0.5*W > H 0.5 3969.19 1292.25 1.54 SAFE Mr Mo 15131.10 7249.52 2.09 SAFE
>
1.25
1.5
ii) Working condition a) F.O.S against Sliding
= = =
b) F.O.S against Overturning
= = =
KLESCET Consultants
0.5*W > H 0.5 4413.04 1292.25 1.71 SAFE Mr Mo 17425.46 7249.52 2.40 SAFE
>
1.25
1.5
Abutment Design
CHECK FOR BASE PRESSURE
For working condition S.B.C. of soil Total load
W ML
x = Length of footing Total width of footing
ML/W L B B/6
Eccentricity
e
=
150
= = = = = = = =
4758.12 Mr - Mo 17474.75 11681.29 2.455 8.20 5.60 0.93
= =
B/2 - x 0.34 m
kN/m2 kN -
5793.46
kN.m m m m m
< (B/6)
SAFE
Pressure, Max Pressure at Base = = =
(W/BxL)x(1+(6e/B) 150.00/(8.20x5.60)x(1+6x0.34/5.60) 141.92
kN/m2
Min Pressure at Base = = Hence
= < S.B.C
Max Pressure
(W/BxL)x(1-(6e/B) 150.00/(8.20x5.60)x(1-6x0.34/5.60) 65.32
kN/m2 SAFE
For seismic condition S.B.C. of soil Total load
W ML
x = Length of footing Total width of footing
Eccentricity
ML/W L B B/6 e
=
225
= = = = = = = =
4509.31 Mr - Mo 17425.46 8661.55 1.921 8.20 5.60 0.93
= =
B/2 - x 0.88 m
kN/m2 kN -
8763.91
kN.m m m m m
< (B/6)
SAFE
Pressure, Max Pressure at Base = = =
(W/BxL)x(1+(6e/B) 150.00/(8.20x5.60)x(1+6x0.88/5.60) 190.70
kN/m2
Min Pressure at Base = = Hence
Max Pressure
= < S.B.C KLESCET Consultants
(W/BxL)x(1-(6e/B) 150.00/(8.20x5.60)x(1-6x0.88/5.60) 5.70
kN/m2 SAFE
Abutment Design
DESIGN OF RETURN WALL
0.30
FRL=
RL100.773
Due to surcharge
h= 6.25 m Top of footing = RL94.523
Soil parameters KA
= = = =
30 0 88 20
=
18
=
0.309
1). Active Earth Pressure Active Earth pressure, p=
Total Pressure=
0.5 h
0.42 h
1.2*Ka*
0.90 C/s of Return wall
Due to Soil
Ka**h
° ° ° ° kN/m3
= =
Ka 0.309 x
=
34.741 kN/m
= =
x
h 6.25
p x 34.741
h 6.25
2
0.5 0.5
x
= = =
108.565 kN/m 108.565 x cos x 20 102.017 kN/m
Vertical component=
= =
108.565 x sin x 20 37.131 kN/m
Moment @ bottom of Toe=
= =
lever arm h 102.017 x 0.42 x 6.25 267.796 kN.m/m
Horizontal component=
2). Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge = =
Active Pressure due to surcharge
Total Pressure
1.2 1.2
x Earth fill 18 x
=
21.600
= = =
Ka x 1.2 0.309 x 1.2 6.670 kN/m
=
6.670
kN/m2
KLESCET Consultants
h
x x
18 18
Abutment Design
= =
6.670 6.25 41.689 kN/m
KLESCET Consultants
Abutment Design
Horizontal component
= =
41.689 x cos 20 39.175 kN/m
Vertical component
= =
41.689 x sin 20 14.258 kN/m
= =
lever arm 39.175 0.5 x 122.421 kN.m/m
Moment @ bottom of Toe
x
6.25
Total Vertical Comp.Force due to soil & surcharge Total Horizontal comp.Force due to soil & surcharge Total Moment due to soil & surcharge Hight of Dpro at base of wall Therefore "d" available = 0.900 Grade of concrete Grade of Steel According to IRC-21:2000 Design Constants: σcbc Modular Ratio Neutral Axis Factor
= = = 6.250 m 900 mm
= =
25 415
=
8.33 N/mm2
σst m
= =
200 N/mm3 10
k
=
m σcbc/( mσcbc + σst)
= =
Lever Arm Factor
j
Q
=
1-(k/3)
dreq
=
1
8.333
-
+
200
0.294 3
0.90 0.5 x σcbc x j x k
=
0.5
=
1.11
=
x
10 x 8.333 0.29
= Moment Factor
10
=
=
51.390 kN/m 141.192 kN/m 390.217 kN.m/m
x
8.333
390.22 x 1000000 1.11 x 1000
KLESCET Consultants
x
0.90 x
0.29
Abutment Design
Dia of bar Overall Depth Provided Clear Cover Center of reinforcement Effective depth Provided
= = = = = =
594.2 32 900 50 16 834
mm mm mm mm mm mm
KLESCET Consultants
< dreq
SAFE
Abutment Design
Area of Steel Required
=
Area of Steel Required
Minimum reinforcement required
Hence required Diameter of bar
M x 106 j x σst x d
=
390.22 x 1000000 0.902 x 200 x 834.000
=
2593.71 mm2/m
= =
0.12 % of cross sectional area 0.12% x 900 x 1000
=
1080 mm2/m
Ast,req
>
Astmin
Ast
= =
Spacing required Spacing provided
= =
2593.71 mm2/m 32 mm 310.1 125
mm2
Provide 32mm dia bars @125mm C/C Total Steel Provided on Embankment Face
=
6433.98 mm2 SAFE
Check for Shear As per IRC-6:2000, Cl:304.7.1.1.1. Shear Force
V
=
141.192 kN
v
= = = =
141.192 x 1000 x 0.169295
Pt
=
(100 x Ast) / (B x d)
= = = As per IRC-6:2000, Table 12B, Page no 37.
100 x 6433.98 1000 x 834.00 0.771
Design Shear stress
Pt
1000 834
0.37 0.31
c =
0.375151
>
v
x
0.50 c
SAFE
0.771 0.271 0.25
KLESCET Consultants
0.06
0.75
Dirt Wall Design
DESIGN OF DIRT WALL Dirt wall is designed as a cantilever member subjected to following loads 1)Active earth pressure 2)Live load surcharge 3)Braking force 0.4
Live load surcharge
h=
Active earth pressure
0.825 m 0.5 h
0.42
1.2*Ka*
C/s of Dirt wall
h
Ka**h
Height of Dirt wall, h = FRL-Top of Abutment cap FRL= h
=
=
100.773 0.825
99.948 m
h =
Top of Abutment cap= Soil parameters = KA =
30 0 88 20
˚ ˚ ˚ ˚
18 kN/m3 0.309
1). Active Earth Pressure Active Earth pressure, p
Total Pressure
Horizontal component
=
Ka
=
0.309
=
4.586
kN/m2
=
0.5 x
=
0.5
x
p
1.892 kN/m
=
1.892 x cos 1.778
0.825
h
x
4.586
=
=
h
x
0.825
x
kN/m x
x
KLESCET Cosultants
20
100.773 m 0.825
99.948 m
Dirt Wall Design
Vertical component
= =
Moment @ bottom of Dirt wall
= =
1.892 x sin 0.647
x
20
kN/m
lever arm 1.778 x 0.42 x 0.616
0.825
kN.m/m
2). Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge = 1.2 x Earth fill =
ctive Pressure due to surcharge
Total Pressure
1.2 x
=
21.600
=
Ka
18 kN/m2 1.2
x
=
0.309 x
=
6.670
=
6.670 x
=
6.670 x 0.825
=
5.503
x
1.2 x kN/m2 h
kN/m
KLESCET Cosultants
18
Dirt Wall Design
Horizontal component
Vertical component
Moment @ bottom of Dirt wall
=
5.503
cos 20
=
5.171 kN/m
=
5.503
x
sin 20
x
=
1.882
kN/m
=
5.171 x
=
2.133
lever arm 0.5 x
0.825
kN.m/m
3). Braking Force Following Vehicles are considered to act on Dirt Wall a) 70R Bogie b) Class A ( Two Lane ) According to the IRC-21:2000, Cl:214.20, Page no 33, braking force is taken as 20% of actual load of wheel on the span a) 70R Bogie
H 1.2
85.00 2.13
Wheel Load
85.00 1.93
0.825
a= 2.025
In Plan 0.22 0.86
0.86 FOOTING
Minimum Axel width in longitudinal direct
1.37
Effective width of dispersion, beff 1.2a + b1 Braking force acts at 1.2 m above Road level Thickness of wearing coat = 75.0 mm b1 = 0.86 + 2 x 0.075
m (Refer Cl.305.16.2 of IRC:21- 2000) (Refer Cl.214.3 of IRC:6- 2000) =
1.010
m
1.2 x 2.025 + 1.010 = 3.440 beff > Spacing of the wheels (1.2m) hence dispersion width over laps
m
beff =
Total Dispersion Width
=
Tb
=
Total axel load
=
2.13
+ 1.93 + 3.440 /
2
5.780 m
Braking Force(20% of axel load), H Braking Force per metre width
170 kN = =
KLESCET Cosultants
34.0 H/Tb
kN
(Refer Cl.214.2 of IRC:6- 2000)
Dirt Wall Design
=
5.882
kN/m
b) CLASS A (2 No.) 57.0 0.9
Wheel Load
In Plan
57.0 1.8
57.0 1.7
0.25
57.0 1.8
0.25
0.5 Minimum Axel width in longitudinal direct
0.5 1.2
m
b1 =
0.5
+
x 0.075
=
0.650
m
beff =
1.2
x 2.025 + 0.650
=
3.080
m
2
KLESCET Cosultants
Dirt Wall Design
beff > Spacing of the wheels (1.2m) hence dispersion width over laps Total Dispersion Width = 0.5+0.15+0.25+1.8+1.7+1.8+(4.506/2) Tb = 7.740 m Total axel load = 228 kN Braking Force(20% of axel load) = 45.6 kN Braking Force per metre width = 5.891 kN/m Hence Class 'A' 2 Vehicle is critical, hence governs the design lever arm Moment due to Braking = 5.891 x 2.025 = 11.93 kN/m = =
Total Bending Moment
Design S.F
= =
Depth Required
11.93 + 0.616 + 0.616 + 15.295 kN.m/m (1.78+5.17+5.89) 12.840 kN
15.30 x 1000000 1.11 x 1000 117.6 mm
=
dreq
=
Overall Depth Provided Clear Cover Diameter of bar
= = =
400 50 20
mm mm mm
Center of reinforcement
=
10
mm
Effective depth Provided
=
340
mm
Area of Steel Required
0.20% x 400
= =
800.00
Spacing required
=
393
mm
Spacing provided
=
150
mm
Astreq
> dreq
15.30 x 1000000 0.902 x 200 x 340 j st. stress eff.depth 249.38 mm2/m
= =
Astmin
2.133
x
1000
mm2/m
< Ast min
Astreq =
800.000 mm2
Provide 20mm dia bars @150mm C/C Total Steel Provided on Embankment Face = KLESCET Cosultants
2094.40 mm2/m
Dirt Wall Design
SAFE
KLESCET Cosultants
Dirt Wall Design
Check for Shear (Refer IRC-6:2000, Cl.304.7.1.1.1, Shear Force
V
=
v
Design Shear stress
100Ast/(bd)
12.840 kN
=
12.840 x 1000 1000 x 340
=
0.038
=
100 x 2094.40 1000 340 x
=
0.616
N/mm2
0.31 0.23
0.25 As per IRC-6:2000, Table 12B, Page no 37. c = c
>
0.347 v
N/mm2
SAFE
KLESCET Cosultants
x
0.616 0.366 0.25
0.08
0.50
Abutment Design
LOADINGS 70-R Wheeled
170
170
170
1.37
3.05
170 1.37
0.2
120 2.13
120 1.52
80 3.96
6 1.17
RA
RB
RA
=
170 x 6.2 + 170 x 4.83 + 170 x 1.78 + 170 x 0.41 + 120 x -1.72 + 120 x -3.24 + 80x-7.2
=
179
kN
Class A 68
68
68
3
68
3
3
0.2
114 4.3
114 1.2
27
27
3.2
1.1
6 2.8
RA RA
RB =
68 x 6.2 + 68 x 3.2 + 68 x 0.2 + 68 x -2.8 + 114 x -7.1 + 114 x -8.3 + 27x-11.5 + 27 x
=
-324 kN
For two lane of Class A
=
-648.0 kN
350
+
350
=
50
50
50
50
50
50
50
0.653
0.653
0.653
0.653
0.653
0.653
0.653
Class 70 R Tracked Total load =
700 kN
KLESCET Consultants
Abutment Design
4.57 50
50 0.653
50 0.653
50 0.653
0.2 0.453 RA
RA
50 0.653
50 0.653
50 0.653
6 RB
=
50 x 6.2 + 50 x 5.55 + 50 x 5 + 50 x 4.24 + 50 x 3.59 + 50 x 2.94 + 50x2.28
=
247
kN
KLESCET Consultants
Abutment Design
Eccentricity in transverse direction Width of carriageway No of lanes
= =
8.20 m 3.00
1 lane of Class A
0.45 0.5
0.15
1.80 8.20
eT
= =
4.1 2.35 m
1.8
2 lanes of Class A
0.45
0.5
0.15
1.80
1.2
8.20
eT
= =
4.1 0.60 m
3.50
KLESCET Consultants
Abutment Design
3 lanes of Class A
0.45
0.5
1.2
0.15
1.80
1.2
1.80 8.20
eT
= =
4.1 1.15 m
5.25
KLESCET Consultants
1.80
Abutment Design
1 lane of Class 70 R
0.45
0.86
0.15
1.93 8.20
eT
= =
4.1 2.105 m
2.00
1 lane of Class 70 R + 1 lane of Class A
0.45
0.86
0.15
0.5
1.93
1.2
1.80 8.20
500
1.93
500
277
1.88
277
1.80
KLESCET Consultants
Abutment Design
Eccentricity due to load
eT
= =
=
4.1 0.770 m
2.30009
3.33
KLESCET Consultants
Abutment Design
DESIGN OF ABUTMENT WALL The abutment wall is designed as a section subjected to Axial force and Bending moment for the following forces 1) Self weight 2) Dead load from superstructure 3) Vehicular live load from superstructure e= 0.525 4) Braking forces 5) Horizontal forces due to secondary effects 6) Active Earth Pressure 400 700 7) Live load surcharge 300 750 0.8 FRL= RL100.773 Due to surcarge Due to Soil150 0.225 Abutment Cap
h=
6.25 m
400
750 0.5 h
Topof foot RL94.523
1.2*Ka*
99.548
0.42 h Ka**h
5.025 750 94.523
Soil parameters = = = = = Ka = Ca =
1). Self weight 1)Dirt wall
Moment @bottom of Wall 2)Abutment cap Rectangular area Moment @bottom of Wall Triangular Area Moment @bottom of Wall
3)Wall
C/L of wall 30 0 88.4161884 20 18 0.309 0.569
˚ ˚ ˚ ˚ kN/m3
= =
0.4x0.75x1x25 7.5
= =
7.5
= = = = = = =
1.1x0.4x1x25 11 kN/m 11 0.175 x 1.925 0.5x0.35x0.35x1x25 1.53125 1.53125 x 0.491666667 0.752864583
= =
0.75x5.02x1x25 94.21875 kN/m
x
3.94
kN/m
lever arm 0.525 kNm/m
KLESCET Consultants
Abutment Design
2). Dead load from super structure Total, R Load per meter width Wd Long. Moment ( ML )
394.36 = = = = =
(from staad analysis) R 8.20 48.09 kN/m lever arm x Wd e1 48.09 x 0.225 10.82 kNm/m
3). Vehicular live load from super structure Following Vehicular loads are considered Eccentricity, e1= 0.225 m
R/meter Moment Total Type of Load Reaction Rm ML=Rm*e1 in kN R A) Class A( 2 No-647.97 -79.02 -17.78 B) Class A( 3 No-971.95 -118.53 -26.67 C) 70R Tracke 494.83 60.35 13.58 D) 70R -3.97 Wheeled + -144.62 -17.64 Class A (1 No.) D) 70R 4.69 tracked + 170.85 20.84 Class A (1 No.) Hence 70R Wheeled + Class A Vehicle governs the design
Long. Moment ML = Total , R=
13.58 494.83
eT
Resultant
2.35 0.60 2.11 1.15
554 1108 1000 1662
kNm/m kN
Moment Type of Load A) Class A( 1 No B) Class A( 2 No C) 70R Wheele D) Class A( 3 No
E) Class A( 1 0.77 No.) + 70R Wheeled Total transverse moment Total transverse moment/m
1554 = =
MT=Rm*eT 1301.90 664.80 2105.00 1911.30 1196.44 2105.00 kNm 256.71 kNm/m
4). Braking forces (20 % of Axle Load upto 2 Lane & 5 % live load for additional lane.) As IRC-6:2010, horizontal seismic forces in the direction perpendicular to the traffi 20.00 % Total Axial load(kN) 1st 2nd lane
3rd Lane
For Static
5.00% -32.40 -48.60
Force -161.99 -242.99
Type of Load 1) Class A 2 VEH 2) Class A 3 VEH
2 lane -647.97 -971.95
3 lane -647.97 -971.95
20.00% -129.59 -194.39
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(without impact)
Total in Force/A BM at kN bt /m Fdl -161.99 -19.76 -242.99 -29.63
-164.95 -247.43
Abutment Design
3) 70R tracked + Class (1 No.) 4) 70R A Tracked
170.85
170.85
34.17
8.54
42.71
42.71
5.21
43.49
494.83
494.83
98.97
24.74
123.71
123.71
15.09
125.97
-28.92
-7.23
-36.15
5) Class A( 1 -144.62 -145 No.) + 70R Wheeled Effective width of dispersion, 1.2*a+b1 1 for Class A = 0.41 beff= 70R Tracked = 1.00 beff= 70R Wheeled = 1.02 beff=
10.43 11.02 11.04
8.20
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-36.15417 -4.40904 -36.82
Hence bef
Max =
125.97
=
8.20
m
Abutment Design
m Total width of dispersion = 8.20 kN total force/trestle= 24.74 ng. Moment due to braking = 125.97 kNm/m
lever arm for the Braking force(m)=
8.35
lever arm for the secondary forces(m)= 6.275
5). Horizontal forces due to secondary forces Span length Length of Bearing L Width of Bearing B Total depth of Bearing D No. of Steel laminates Thickness of steel laminate Shear Modulus G Modulus of elasticity of concr E Co efficient of thermal expans (IRC 6-2010, Cl 218.4, Page 46) Maximum Temperature (IRC 6-2010, Fig 8, Page 42) Minimum Temperature (IRC 6-2010, Fig 9, Page 43) Temperatue difference t
= = = = = = = = =
6000 630 400 50 4 3 1 25000.0 1.17E-05
mm mm mm mm
Strain due to Temperature
=
Deformation due to Temperature
= = =
Shear deformation
= =
Deformation / Depth 0.16
Force on each bearing
= = =
Shear deformation x Shear modulus
mm N/mm2 N/mm2 / oC
=
37.5 oC
=
10 oC
=
27.5 oC
Number of bearings Force on abutment Force / meter length along abutment
= = =
Moment @bottom of Wall
= =
0.00032 Strain x 0.00032 x 1.93 mm
5067.56 N 5.1 kN 5 25.34 kN 3.09 kN/m 3.09
x 6.275 19.39 kN-m/m
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Span 6000
x Area of bearing
Abutment Design
6). Active Earth Pressure Active Earth pressure, p
18 kN/m2
= = =
Ka 0.309 34.741
Total Pressure
= = =
0.5 p x 0.5 34.741 108.565 kN/m
Horizontal component
= =
Vertical component
= =
108.565 37.131
ment @ bottom of Abutment
= =
lever arm 102.017 0.42 6.25 267.80 kN.m/m
= = = = =
1.2 1.2 21.600 Ka 6.670
Earth fill 18 x kN/m2 1.2 x xx kN/m2
= = = = = = =
6.670 6.670 41.689 41.689 39.175 41.689 14.258
x
= =
39.175 122.421
=
274.08
=
566.59
7). Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge
Active Pressure due to
Total Pressure
Horizontal component Vertical component
Moment @ bottom of Abutment
Total Vertical Force, P Total Longitudinal Moment ML
h 6.25
h 6.25
108.565 cos 20 102.017 kN/m sin kN/m
x
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h 6.25 kN/m cos x kN/m sin kN/m
20
18
x
20 20
lever arm 0.5 6.25 kN.m/m
kN/m kNm/m
Abutment Design
DESIGN OF ABUTMENT AS WALL Longitudinal moment
ML
Effective depth required
=
dreqd.
Overall depth provided Clear Cover Diameter of bar Half dia. of Bar Effective depth provided Area of Steel Required
Ast Spacing required Spacing provided
=
566.59 kNm/m
√(M /Q.b)
=
566.59 x 1000000 1.11 x 1000
= = = = = =
715.96 825.00 75.00 25 12.50 737.50
=
566.59 x 1000000 0.902 x 200 x
=
4258.8
= =
mm mm mm mm mm mm
> dreq SAFE 737.50
mm2
115 100 mm
Provide 25mm dia bars @100mm C/C Total Steel Provided
=
4908.74 mm2/m
KLESCET Consultants
SAFE
Abutment Design
Check for Shear (Refer IRC-6:2000, Cl.304.7.1.1.1, Shear Force
V
v
Design Shear stress
100Ast/(bd)
=
141.192 kN/m
=
141.192 x 1000 1000 x 738
=
0.19
N/mm2
=
100 1000
x 4908.74 x 737.5
=
0.666
0.42 0.37
0.75 As per IRC-6:2000, Table 12B, Page no 37. c
=
c
>
0.353 v
N/mm2 SAFE
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x
0.666 -0.084 0.25
0.05
1.00
Abutment Design
CALCULATION OF ACTIVE EARTH PRESSURE
i) Static case Active earth pressure is calculated using Columb's theory as per IRC:78 - 2000, Cl.710.1.3
Soil parameters
Unit weight of soil Angle of internal friction of soil Surcharge angle Angle of inclination of wall from horizontal face Angle of friction between wall and soil
= = = = =
18 30 0 88 20
kN/m3 ° ° ° °
F.L Due to surcarge
RL 100.773
Due to Soil
7.15 m
h=
0.5 h
0.42 h
Found. Lvl 1.2 x Ka x
RL 93.623
Ka x x h
Static Earth Pressure Diagram Active earth pressure coefficient Ka
=
sin 2 (- ) sin 2 x
sin ( - )
1
= 0.930
x
1
+
0.309
Active Earth Pressure = = =
Ka x 0.309 x 39.743 kN/m2
PA
= = =
0.5 p x x 0.5 x 39.743 x 142.08 kN/m
Horizontal component
= = =
Vertical component
= =
Active Earth pressure
Total Static Pressure
p
sin ( + ) sin ( - ) sin ( - ) sin ( + )
2
0.7735451475 0.99923607x
=
+
x x
PA
cos 20 x 142.083 x 0.94 133.514 kN/m PA
x
142.083 x
sin 20 0.34
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h 7.15
h 7.15
0.766 x
0.5
0.930 x
1.000
2
Abutment Design
x
=
48.595
kN/m
KLESCET Consultants
Abutment Design
Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge = = = Active Pressure due to surcharge Total Pressure
Horizontal component
Vertical component
1.2 x Earth fill 1.2 x 18 21.600 kN/m2
= = = = =
Ka 1.2 x x 6.670 kN/m 6.670 h x 6.670 x 7.15 47.692 kN/m
= = =
47.692 47.692 44.816
cos 20 0.94 kN/m
= = =
47.692 sin 20 x 47.692 x 0.34 16.312xkN/m
x x
Total Vertical Comp.Force due to active earth pressure & live load surcharge Total Horizontal comp.Force due to active earth pressure & live load surcharge For
8.20
18
=
64.907
kN/m
=
178.330 kN/m
=
532.235 kN
=
1462.304 kN
m carrigeway
Total Vertical Comp.Force due to active earth pressure & live load surcharge Total Horizontal comp.Force due to soil & surcharge
ii) Seismic case Seismic active earth pressure coefficient Ca
=
( 1 + Av ) cos2 ( - - )
x
cos cos cos ( + + ) 2
1
+
1 sin ( + ) sin (- - ) cos ( - ) cos ( + + )
Where,
Ca
= =
13.6
=
1.036 0.794
=
Total AEP due to Static and Siesmic
tan-1(Ah/1-Av)
PAE
°
x
1
1 + 0.766 x 0.999618
0.569
=
0.5 x x h2 x Ca
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2
0.282 0.817
2
Abutment Design
= =
0.5x18x7.150x7.150x0.569 261.8 kN/m
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Abutment Design
F.L RL 100.773
Due to surcarge
Due to Soil
7.15 m
h=
0.66 h
0.5 h
Found. Lvl 0.2 x 1.2 x x Ca
RL 93.623
(Ca - Ka) x x h
Seismic Earth Pressure Diagram
Active Earth pressure
Total Seismic Pressure
p
PAEQ
Horizontal component
Vertical component
= =
(Ca - Ka) x 0.260 x
=
33.491
=
0.5
x
h 7.15
x
h
x
kN/m2
p
x
= =
0.5 x 33.491 x 119.73 kN/m
= = =
PAEQ
x
PAEQ
x
= = =
Live load Surcharge (Refer IRC:78- 2000, Cl.710.4.4, Pg.No.55) Live load Surcharge q = =
7.15
cos 20 119.731 x 0.94 112.511 kN/m sin 20
119.731 x 0.34 40.950 kN/m
0.2 0.2
=
4.320
=
Ca
1.2 1.2
x x
x Earth fill
18
x
kN/m
2
(Refer IRC:6- 2010, Table 1, Pg.No.6) Active Earth pressure due to surcharge
p
= = Horizontal component
Vertical component
q
x
h
x
0.569 x x 17.58 kN/m
7.15
= = =
17.58 17.58 16.52
= = =
17.58 sin 20 x 17.58 x 0.34 6.01xkN/m
Total Vertical Comp.Force due to active earth pressure & live load surcharge
cos 20 0.94 x kN/m x
=
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46.962
kN/m
Abutment Design
Total Horizontal comp.Force due to active earth pressure & live load surcharge For
8.20
=
129.027 kN/m
=
385.088 kN
=
1058.020 kN
m carrigeway
Total Vertical Comp.Force due to active earth pressure & live load surcharge Total Horizontal comp.Force due to active earth pressure & live load surcharge
KLESCET Consultants
Abutment Design
DESIGN OF ABUTMENT STEM The length of column (Height) The following details obtained from Abutment Stem Design: (Nd) Load
=
6250mm
=
274.08kN
Moment
(Md)
=
566.59kN
Stem thickness
(h)
=
900mm
Breadth
(b)
=
1000mm
Grade of concrete
=
M25
Grade of steel
=
Fe415
Tension face reinforcement
=
20
Area of
20 mm dia. bars
Compression face reinforcement
@
=
180 c/c 314sq.mm
=
12
No. of bars in tension face
=
11.11
[or]
12
No. of bars in comp. face Area of steel in tension face ( AS )
=
5.56
[or]
6
=
3770sq.mm
Area of steel in comp. face ( A'S )
=
679sq.mm
Area of
@
12 mm dia. bars
e
Modular ratio
180 c/c 113sq.mm
=
10
As per page 365 of Reynold's Handbook To find eccentricity, Md e = Nd h 6 h 2 3h 2 Therefore,
e
=
566.59
x 274.08 900
=
6 900
= = >
1000
2 3
x
900
2 h/2
>
=
2067.2mm
=
150.0mm
=
450.0mm
=
1350.0mm
3h/2
Effective cover to tensile steel
=
Effective depth
=
50
+
20
=
60mm
=
840mm
2 900 - 60 fcu x h = 900
d = 840 60 b=
Assumed depth of N.A
1000 =
243.00mm
SAFE
KLESCET Consultants
0%
Abutment Design
K1
= b.x
=
1,000 x 243
=
243000sq.mm
To determine the centroid of stressed area K1.x + e.As.d + (e-1) A's.d' 1/2 x = K1 + e.As + (e-1)A's 0.50x243,000x243 + 10x3,770x840 + (10x1.5-1)x679x60
=
1
=
2
=
3
=
= 212.83mm
243,000 + 10x3,770 +1.5x(10-1)x679
e-x
+
d
x
1-
2d
1
x
1-
d'
243
1-
2x840
=
x
+
840
=
3d
(e - 1)
2,067.25 - 212.83
=
(10x1.5-1) x
1-
243 3x840 60 243
Compressive stress in concrete Nd.1 Fcs
=
2.b.d + 3.A's.
1-
274.08 =
x
d'
1000
0.131x1,000x840 + 10.543x679x
d x
3.208 1-
60 840
= 7.551Mpa
FC
=
=
=
Nd bx+eAs+(e-1)A'S 274.08x 1000 1000x243+10x3,769.91+(10-1)678.58 274077.95 286806.37
= 0.956Mpa Fcs max
=
( Fcs + FC )
=
7.55
+
0.96
=
8.51MPa
>
8.33Mpa
UNSAFE
KLESCET Consultants
1
= 3.208
= 0.131
= 10.543
Abutment Design
Calculation of Tensile stress in steel Permissible tensile stress in steel = fcs (0.5 K1 + b3 A's) - Nd fst = As =
200.00Mpa
7.551x (0.5x243,000 + 10.543x679) - 274
1000
3769.9111843078
= 184.992Mpa fst max = ( fst + Fc ) 184.99
=
= 184.04MPa
-
0.96
<
200.00Mpa
SAFE Check for the depth of Neutral Axis: Actual depth of Neutral Axis based on the stress level in concrete and steel and the effective depth is calculated from the formula d xa
=
1+
840 fst
=
e.fcs
% error is assumed N.A
=
184.99
1+
=
243.49mm
10x7.55 243.49 - 243.00
x
243.49
100
=
0.20%
<
5 %
SAFE
CHECK FOR MINIMUM REINFORCEMANT IN THE SECTION : The length of column Min. radius of gyration
r
Effective length factor
=
6250.0mm
=
sqrt(I/A)
=
sqrt[(1,000x900^3) / (12x900x1,000)]
=
259.8mm
=
1.75
(Refer IRC:21-2000, Cl.306.1, Table 13) leff
Effective length
= leff/r =
Slenderness ratio,
Min. steel in pedestal
1.75 x 6,250
=
42.10
=
0.30%
(Refer IRC:21-2000, Cl.306.2.2, Pg.No.59)
20 f
Actual area of steel provided
180 c/c +
10937.5mm SHORT COLUMN
of gross area
0.30 x 1,000 x 900 =
(Ast + Asc)(
=
10,937.50 / 259.81
12 f
2700sq.mm
180 c/c )
= 3769.91118431 >
=
100
+
678.58401 =
2700sq.mm
KLESCET Consultants
SAFE
4448sq.mm
Abutment Design
SEISMIC COEFFICIENT Seismic coefficient is calculated as per provisions made in IRC 6 - 2010, IS 1893 - 1984 and IITK guidelines. Soil type = Medium soil Zone number = V Zone factor Z = 0.36 (Refer IRC 6 -2010, Table 6, Pg.No.47) Importance factor I = 1.20 (Refer IRC 6 -2010, Table 7, Pg.No.51) Reduction factor R = 2.50 (Refer IRC 6 -2010, Table 8, Pg.No.52) CALCULATION OF TIME PERIOD (Refer IRC 6 -2000, Appendix - 2, Pg.No.61) T = 2√D/(1000F) Where, T = Fundamental period of the pier/abutment in secs for horizontal vibrations D = Appropriate dead load of the superstructure and live load in kN Horizontal force in kN required to be applied at the centre of mass of superstructure for one mm deflection at the top of the pier/abutment F = along the considered direction of horizontal force. = = = = =
Grade of concrete Dead Load Live load Self Weight of Abutment Total ( w )
25 394.36 494.83 983.87 1873.07
kN kN kN kN
Height of abutment
L
=
5425 mm
Breadth of abutment
B
=
8200 mm
Thickness of abutment wall
t
=
750 mm
Young's Modulus
E
=
5000√Fck
=
25000
=
(B x t3 / 12)
Moment of inertia
Igr
=
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N/mm2
8200 x 4.22E+08 12
Abutment Design
= T=2√W/(1000F) FL3 / 3EI F
=
1
=
3EI/L3
=
T
3
x25000.00 x2.88E+11
1.60E+011
=
135.418635 kN
=
0.235 Sec
Sa /g = 2.50 ( Refer IRC:6-2010, Cl.219.5.1, Pg.No.50) Design horizontal seismic coefficient Z I Sa Ah = 2Rg = =
(0.36x1.2x2.5) 2x2.5 0.216
Av is taken as (1/2)Ah as per IS: 1893: 1984 Av
=
0.108
KLESCET Consultants
2.88E+11 mm4
Abutment Design
For
8.20 m carrigeway
Seismic force at bearing level
=
0.216 x 394.36
= Longitudinal moment upto footing top level
=
85.18 kN
85.18
=
Longitudinal moment upto footing bottom level
=
x
6.325
538.77 kN-m
85.18
=
x
7.225
615.44 kN-m
Per running meter carriage way Seismic force at bearing level
=
10.39 kN/m
Longitudinal moment upto footing top level
=
65.70 kN/m
Longitudinal moment upto footing bottom level
=
75.05 kN/m
KLESCET Consultants
Abutment Design
DESIGN OF FOOTING Abutment hight above footing Unit weight of soil Unit weight of concrete
= = =
B
1.5
6.3 m 18.0 kN/m3 25.0 kN/m3
1.0
3.2
A 0.9
0.9
0.9 5.6 65.319 kN/m2
141.916 kN/m2 85.836 kN/m2 99.514 kN/m2 Upward pressure diagram 112.5 kN/ 11.655kN/
m
22.5 kN/
mm
22.5 kN/
mm
m
Downward pressure diagram
Design of toe slab Outstand w.r.t face of Column Design Bending Moment at face of support
dreqd.
Overall depth provided Clear Cover Diameter of bar Half dia. of Bar Effective depth provided
= =
3.2 m 144.73 + 509.51 triangle rectangle
=
539.05
=
√(M /Q.b)
115.20 rectangle
kN-m/m
=
539.05 x 1000000 1.11 x 1000
= = = = = =
698.34 900.00 75.00 25 12.50 812.50
=
539.05 x 0.902 x
=
3677.8
mm mm mm mm mm mm
> dreq
SAFE Are of Steel Required
Ast Spacing required Spacing provided
= =
1000000 200 x
812.50
mm2
133 120 mm
Provide 25mm dia bars @120mm C/C Total Steel Provided =
4090.62
mm2/m
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SAFE
Abutment Design
Check for shear stress Shear is critical @ distance 'd' from face of support Centre line of abutment critcal section 0.8125
2.3875
99.51
m
141.916
kN/m2
kN/m
2
110.280 kN/m2 3.2 Shear Force across the critical section
V
=
37.77
+
triangle
Developed Shear Stress
=
247.34
=
V bd
= = 100 As
=
bd
53.72
rectangle
rectangle
kN/m
247.34 x 1000 1000 x 812.50 0.30
N/mm2
4090.62 xx 1000 x
x
=
263.3
0.50
100 812.50
%
Permissible Shear Stress (Refer IRC:21 -2000,Cl.304.7.1.3.3, Table 12B, Pg.No. 37) For 100 As/bd 0.50 0.75 Allowable Shear Stress, c=
0.311
MPa
c (Mpa) 0.31 0.37
>
SAFE
Design of heel slab Outstand w.r.t face of Column Design Bending Moment at the face of support
=
=
1.5
126.56 +
m
13.11
+
8.74 7.69
KLESCET Consultants
73.48
Abutment Design
=
67.24
=
√(M /Q.b)
=
67.24 1.11
=
246.64
Overall depth provided Clear Cover Diameter of bar Half dia. of Bar Effective depth provided
= = = = =
900.00 75.00
Are of Steel Required
=
67.24 0.902 j
Ast
=
456.22
Ast(min)
=
0.12%
=
1080
mm2/m
=
1080
mm2/m
dreqd.
Ast,required Spacing required Spacing provided
kN-m/m
x 1000000 1000 x
mm
mm mm 16 mm 8.00 mm 817.00 mm
= =
> dreq
SAFE
1000000 817 x 200 xx st. stress eff depth
x
mm2/m 900
x
< Ast(min) x
1000
186 150 mm
Provide 16mm dia bars @150mm C/C Total Steel Provided Ast,provided
=
1340.41
SAFE
mm2/m
Check for shear stress Shear is critical @ face of support critical section 1.5
65.32
kN/m2 85.8
kN/m2
1.5 Shear Force across the critical section
V
=
168.75
=
89.13
+ 33.75 kN/m
KLESCET Consultants
113.37
Abutment Design
Developed Shear Stress
=
V bd
=
89.13 1000
=
0.11
1000 817
x x
N/mm2
(As per IRC: 21-2000, Table 12A) 100 As
=
bd
=
1340.41 x 1000 x 0.164
100 817
x
%
Permissible Shear Stress (Refer IRC:21 -2000,Cl.304.7.1.3.3, Table 12B, Pg.No. 37) For 100 As/bd
Allowable Shear Stress, c=
0.204
c (Mpa)
0.15
0.20
0.25
0.23
MPa
>
KLESCET Consultants
SAFE
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