1.
Design Condition
1.1 Type : xxx-Type (H=xm, B=m) [Superstructure Type : PSC(Span=50m)]
1.2 Foundation Type :
Unit Weight of Abutment Materials =
1.3 Design Load
1) Dead Load
A) Ground
Ground Soil Unit Weight (γ1) : 18 KN/m2
N-Value at pile end (N) : = 10 (Soft Soil)
B) Back Fill
Self Unit Weight (γ2) : 18 KN/m2
Shear Resistance Angle (φ) : 35
2) Live Load : IRC class A truck
3) Earth Pressure
A) Coefficient of Active Earth Pressure at Ordinary Time ( Coulomb Earth Pressure )
Sin ( )
2
Ka 2
Sin ( ) Sin ( )
Sin 2 Sin ( ) 1
Sin ( ) Sin ( )
B) Coefficient of Active Earth Pressure at Seismic ( Mononbe-Okabe Formula )
Sin ( ' )
2
Ka 2
Sin( ) Sin( ' )
Cos ' Sin Sin( ' )1
2
Sin( ' ) Sin( )
4) Impact Factor ( Span L = 50.00 m )
Using "IRS 6 2010 loads and stress" for specifying Loads on superstructure and substructure:
impact factor is taken as 10% as section 208
5) longitudinal force
A) Brake Load: IRS 6 2010 loads and stress section 211 (Breaking effect is invariablly greater then tractive effect)
B) Start Load : (Also called Tractive effort)
C) Frictional resistance offered to the movement of free bearing due to change of tempurature or any other cause
6) Surcharge Load
qL = 35 KN/m² (Live Load)
qD = 15 KN/m² (Dead Load)
7) Seismic Load
Using IRC:6 - 2010 Section 219 for seismic load:
Design Horizontal Seismic Coefficient:
for time period 𝑇=2∗√(𝐷/1000𝐹) D= superstructre dead load+ live load (KN)
F= horizontal force in KN for 1 mm deflection of abutment
D= 5349.234 KN
F= 194.140 KN I= 6.252
Kh = 0.06 x 1.200 = 0.072 (For EarthPressure: Kh =(Z/2 x (I)/R)(Z=0.36, Zone V, I=1.2, R=3)
kh = 0.072 x 2.5 = 0.180 (Inertia force calculation of superstructure, (Sa/g = 2.5)
8) Temperature Variation
1.4 Used Material and Strength
1) Concrete Design strength : fck = 30 MPa
2) Rebar Yield Strength : fy = 415 MPa
3) Bearing ( xxxx Bearing ) - Bearing Friction Coefficient (μm) : 0.150
2. Assumed Section b1 b2
Approch slab
b3 b4 height up to bearing H = 9.630 m
Dh= bearing height Bh = 0.500 m
①
Deck height Dh = 3.750 m
total height Ht = 13.880 m
Length of Abutment L = 4.500 m
A b1 = 0.500 m
A A
b2 = 1.350 m
b3 = 0.600 m
b4 = 0.750 m 569
ⓐ ② b5 = 1.850 m
H= 9.630 b6 = 2.900 m
b7 = 3.700 m
depth of foundation Df = 1.000 m
Aproach Slab BA = 8.300 m (top width of Girder)
LA = 3.700 m (Length of back fill)
B B b = 8.450
b5
③ ④ Df= 1.00 m
O
b7= 3.700 b6= 2.900
3.Load Calculation
3.1 Abutment and Backfill Self Weight
1) Volume
① b1 x ( Dh + Bh ) x L = 9.563
② b5 x Ht x H = 80.170
③ ( B7 + B5 ) Df x T = 24.975
④ x Df x T = 13.050
b6
ⓐ B x ( H1 + H ) x L = 231.102
2) Self Weight & Moment
Vertical force and momnet Horizental force and moment
Classification Volume Unit weight
V X M H Y M
① 9.563 24.5 234.28 4.500 1,054.27 42.170625 12.755 537.88632
② 80.170 24.5 1,964.16 3.825 7,512.91 353.5486 5.815 2055.8851
Abut. Self ③ 24.975 24.5 611.89 5.675 3,472.46 110.13975 0.5 55.069875
Wt.
④ 13.050 24.5 319.73 1.45 463.60 57.5505 0.5 28.77525
Σ 2,198.44 12,503.24 563.40947 2677.6165
ⓐ 231.102 18 4,159.84 6.6 27454.918 748.77048 7.94 5945.2376
Backfill
Σ 4,159.84 27454.918 748.77048 5945.2376
3.2 Surcharge Load
1) Dead Load
Vd = 15.00 × 4.50 × 3.700 = 249.750 KN
MVd = Vd × b6+b2+(b1+b7)/2 = 1585.9125 KN·m
Horizontal Force due to Surcharge at seismic condition :
Vd h = 249.75 × 0.180 = 44.955 KN
Md h = Vd × Ht+Df = 668.93 KN·m
2) Live Load
(1) Single Track Loading
Vql1 = 35.00 × 4.150 × 4.200 = 610 KN
Mvql1 = Vql1 × b6+b2+(b1+b7)/2 = 3,874 KN·m
(2) Double Track Loading
Vql1 = 35.00 × 8.300 × 4.200 = 1,220 KN
Mvql1 = Vql1 × b6+b2+(b1+b7)/2 = 7,748 KN·m
3.3 Superstructure Load
1) Dead Load (Superstructure Calculation Reference)
Clasification G1 G2 G3 G4 G5 Total Remarks
Reaction Force 5246.582
2) Live Load (except Impact, Superstructure Calculation Reference) - Single Track
Clasification G1 G2 G3 G4 G5 Total Remarks
Reaction Force 513.262
3.4 Design Horizontal Force (Longitudinal Direction Horizontal Force)
1) Braking Load considering braking load only (breaking load > tracting load)
The longitudinal force for braking the class A
vehicle is maximum and is given by HBr = 0.20 Wt, where 0.20 is the
coefficient and Wt is the weight of the vehicle directly on the span = 554.000 KN (Total Wt of the IRC class A Tr vehicle 2*27+2*114)
Effect due to class A loading will be less. Hence HBr = = 110.800 KN
this acts 1.2 m above deck level, i.e at a distance from abut. base of
Moment due to braking about abutment base = 1781.664 KN-m
2) Seismic Load
Seismic Force = Kh x Dead load of super structure
= 0.180 x 5246.582
= 944.385 KN
3.5 Earth Pressure Coefficient & earth pressure
1) Coefficient of Active Earth Pressure at Ordinary Time ( Coulomb Formula )
φ (Angle of internal friction of soil) = 35 β = 90 (Slope of backfill) 0.61087
δ (Friction between wall and soil) = 23 α = 0 (Inclination of earth face of wall) 0.40724
∴ Ka = 0.244 0.6710100717 1 0.9182161 1 0.4881805 0.9182161069 2.9899648
2) Coefficient of Active Earth Pressure at Seismic ( Mononbe-Okabe Formula )
φ (Angle of internal friction of soil) = 35 θ = 0.072 tan -1 [ Kh / (1-Kv) ] 0.611
δ (Friction between wall and soil) = 23 β = 90 (Angle between backwall and vertical plan) 0.407
α = 0 (Inclination of earth face of wall)
Kh (Horizontal Seismic coefficient) = 0.072 Kv = 0 (Vertical seismic coefficient)
γ (Unit weight of soil) = 20.00 KN/㎥ i (Slope of backfill)
∴ Kae = 0.287
0.737 0.99741803 1.000 0.8874012 1 0.4368516 0.8874011931
Earth pressure
ｑd = 15.00 KN/m² ｑl = 35 KN/m²
1) Active Earth Pressure at Ordinary Time
A) Earth pressure due to surcharge load
Pa1d = Ka x qd x H x L = 229 KN
Pa1L = Ka x ql x H x L = 533 KN
y1 = H /2 = 6.94 m
B) Earth Pressure
Pa2 = 1/2 x Ka x γ x H 2
x L = 1,904 KN
y2 = H /3 = 4.627 m
2) Active Earth Pressure at Seismic
A) Earth pressure due to surcharge load
Paed = Kae x qd x H x L = 269 KN
PaeL = Kae x ql x H x L = 627 KN
Ye1 = H /2 = 6.94 m
B) Earth Pressure
Pae = 1/2 x Kae x (1-Kv) x γ x H 2
x L = 2,488 KN
3.1.7 Foundation design
i) Service load
A. Load Combination
Load Case 1 = 1.0·Dead Load + 1.0· Earth Pressure
Load Case 2 = 1.0·Dead Load + 1.0· Earth Pressure + 1.0·Live Load (Impact)
Load Case 3 = 1.0·Dead Load+1.0·Earth Pressure+1.0·Live Load (Impact)+1.0·Brake Load
Load Case 4 = 1.0·Dead Load + 1.0· Earth Pressure at Seismic + 1.0·Seismic Load
B.Load calculation
Load Case 1 = 1.0·Dead Load + 1.0· Earth Pressure
Vertical Force and Moment Horizontal Force and Moment
Load
L.F. V x Mv L.F. H y Mh
Abutment 1 2,198.44 12,503.24
self weight Backfill 1 4,159.84 27454.9176
buoyance
super Dead 1 5246.5816 3.65 19150.02284
structure Live
surcharge Dead 1 249.75 6.35 1585.9125
load LIve
surcharge PD 1 228.6036 6.94 1586.509
earth
pressure PL
Earthpressure 1 1903.811 4.626667 8808.298
Total ∑V= 11,854.61 ∑mv= 60,694.09 ∑H= 2132.414 ∑Mh= 10394.807
Load Case 2 = 1.0·Dead Load + 1.0· Earth Pressure + 1.0·Live Load (Impact)
Vertical Force and Moment Horizontal Force and Moment
Load
L.F. V x Mv L.F. H y Mh
Abutment 1 2,198.44 12,503.24
self weight Backfill 1 4,159.84 27454.9176
buoyance
super Dead 1 5246.5816 3.65 19150.02284
structure Live 1 513.262 3.65 1873.4063
surcharge Dead 1 249.75 6.35 1585.9125
load LIve 1 610.05 6.35 3873.8175
surcharge PD 1 228.6036 6.94 1586.509
earth
pressure PL 1 533.4084 6.94 3701.854
Earthpressure 1 1903.811 4.626667 8808.298
Total ∑V= 12,367.87 ∑mv= 62,567.50 ∑H= 2665.823 ∑Mh= 14096.661
Load Case 3 = 1.0·Dead Load+1.0·Earth Pressure+1.0·Live Load (Impact)+1.0·Brake Load
Vertical Force and Moment Horizontal Force and Moment
Load
L.F. V x Mv L.F. H y Mh
Abutment 1 2,198.44 12,503.24
self weight Backfill 1 4,159.84 27454.9176
buoyance
super Dead 1 5246.5816 3.65 19150.02284
structure Live 1 513.262 3.65 1873.4063
surcharge Dead 1 249.75 6.35 1585.9125
load LIve 1 610.05 6.35 3873.8175
surcharge PD 1 228.6036 6.94 1586.509
earth
pressure PL 1 533.4084 6.94 3701.854
Earthpressure 1 1903.811 4.626667 8808.298
Break Load 1 110.8 1781.664
Total ∑V= 12,977.92 ∑mv= 66,441.31 ∑H= 2665.823 ∑Mh= 14096.661
Load Case 4 = 1.0·Dead Load + 1.0· Earth Pressure at Seismic + 1.0·Seismic Load
Vertical Force and Moment Horizontal Force and Moment
Load
L.F. V x Mv L.F. H y Mh
Abutment 1 2,198.44 12,503.24 1 563.4095 2677.617
self weight Backfill 1 4,159.84 27454.9176 1 748.7705 5945.238
buoyance
super Dead 1 5246.5816 3.65 19150.02284 1 944.3847 10.63 10038.809
structure Live
surcharge Dead 1 249.75 6.35 1585.9125 1 44.955 668.930
load LIve
surcharge PD 1 228.6036 6.94 1586.509
earth
pressure PL
Earthpressure 1 1903.811 4.626667 8808.298
Total ∑V= 11,854.61 ∑mv= 60,694.09 ∑H= 2132.414 ∑Mh= 10394.807
C) Summary Of Load
Classification V H Mo Remark
LOAD CASE 1 11854.608 2132.414 100385.000
LOAD CASE 2 12367.870 2665.823 3783.415 Ordinary Time
LOAD CASE 3 12977.920 2665.823 2487.059
LOAD CASE 4 11854.608 2132.414 -213.565 Seismic
Max 12977.920 2665.823 100385.000
ii) Ultimate load
A. Load Combination
Load Case 1 = 1.4·Dead Load + 1.7· Earth Pressure
Load Case 2 = 1.4·Dead Load + 1.7· Earth Pressure + 2.0·Live Load (Impact)
Load Case 3 = 1.7 Dead Load + 1.7 Earth Pressure + 1.7 Live Load (Impact)
Load Case 4 = 1.7·Dead Load+1.7·Earth Pressure+1.4·Live Load (Impact)+1.4·Brake Load
Load Case 5 = 1·Dead Load + 1.0· Earth Pressure at Seismic + 1.0·Seismic Load
B.Load calculation
Load Case 1 = 1.4·Dead Load + 1.7· Earth Pressure
Vertical Force and Moment Horizontal Force and Moment
Load
L.F. V x Mv L.F. H y Mh
Abutment 1.4 3,077.82 17,504.53
self weight Backfill 1.4 5,823.77 38,436.88
buoyance
super Dead 1.4 7,345.21 3.65 37,534.04
structure Live
surcharge Dead 1.4 349.65 6.35 3,108.39
load LIve
surcharge PD 1.7 388.63 6.94 2,697.07
earth
pressure PL
Earthpressure 1.7 3,236.48 4.63 14,974.11
Total ∑V= 16,596.45 ∑mv= 96,583.8 ∑H= 3,625.10 ∑Mh= 17,671.17
Load Case 2 = 1.4·Dead Load + 1.7· Earth Pressure + 2.0·Live Load (Impact)
Vertical Force and Moment Horizontal Force and Moment
Load
L.F. V x Mv L.F. H y Mh
Abutment 1.4 3,077.816 17,504.53
self weight Backfill 1.4 5,823.770 38,436.88
buoyance
super Dead 1.4 7,345.214 3.65 37,534.04
structure Live 2 1,026.524 3.65 7,493.63
surcharge Dead 1.4 349.650 6.35 3,108.39
load LIve 2 1,220.100 6.35 15,495.27
surcharge PD 1.7 388.626 6.940 2697.065
earth
pressure PL 1.7 163.223 6.940 1132.767
Earthpressure 1.7 3236.478 4.627 14974.106
Total ∑V= 17,622.97 ∑mv= 104,077.5 ∑H= 3788.3274 ∑Mh= 18803.939082
Load Case 3 = 1.7 Dead Load + 1.7 Earth Pressure + 1.7 Live Load (Impact)
Vertical Force and Moment Horizontal Force and Moment
Load
L.F. V x Mv L.F. H y Mh
Abutment 1.7 3,737.35 3,737.35
self weight Backfill 1.7 7,071.72 46,673.36
buoyance
super Dead 1.7 8,919.19 3.65 32,555.04
structure Live 1.7 872.55 3.65 3,184.79
surcharge Dead 1.7 424.58 6.35 2,696.05
load LIve 1.7 1,037.09 6.35 6,585.49
surcharge PD 1.7 388.626 6.940 2697.065
earth
pressure PL 1.7 163.223 6.940 1132.767
Earthpressure 1.7 3236.478 4.627 14974.106
Total ∑V= 21,025.38 ∑mv= 88,846.6 ∑H= 3788.327 ∑Mh= 18803.939
Load Case 4 = 1.7·Dead Load+1.7·Earth Pressure+1.4·Live Load (Impact)+1.4·Brake Load
Vertical Force and Moment Horizontal Force and Moment
Load
L.F. V x Mv L.F. H y Mh
Abutment 1.7 3,737.35 3,737.35
self weight Backfill 1.7 7,071.72 46673.35992
buoyance
super Dead 1.7 8,919.19 3.65 32,555.04
structure Live 1.4 718.57 3.65 2,622.77
surcharge Dead 1.7 424.58 6.35 2,696.05
load LIve 1.4 854.07 6.35 5,423.34
surcharge PD 1.7 388.626 6.940 2697.065
earth
pressure PL 1.7 163.22297 6.940 1132.767
Earthpressure 1.7 3236.4783 4.627 14974.106
Break Load 1.4 155.12 2494.330
Total ∑V= 21,725.47 ∑mv= 93,707.9 ∑H= 3943.447 ∑Mh= 21298.269
Load Case 5 = 1·Dead Load + 1.0· Earth Pressure at Seismic + 1.0·Seismic Load
Vertical Force and Moment Horizontal Force and Moment
Load
L.F. V x Mv L.F. H y Mh
Abutment 1 3,077.82 17,504.53 1 563.409 2677.617
self weight Backfill 1 5,823.77 38436.88464 1 748.770 5945.238
buoyance
super Dead 1 7345.21424 3.65 26810.03198 1 944.385 10.630 10038.809
structure Live
surcharge Dead 1 349.65 6.35 2220.2775 1 44.955 668.930
load LIve
surcharge PD 1 388.626 6.940 2697.065
earth
pressure PL
Earthpressure 1 3236.478 4.627 14974.106
Total ∑V= 16,596.45 ∑mv= 84,971.72 ∑H= 3625.1044 ∑Mh= 17671.1716674
C) Summary Of Load
Classification V H Mo Remark
LOAD CASE 1 16596.451 3625.104 -8792.672
LOAD CASE 2 17622.975 3788.327 -10816.466
Ordinary Time
LOAD CASE 3 21025.379 3788.327 18789.574
LOAD CASE 4 21725.470 3943.447 19380.468
LOAD CASE 5 16,596.45 3625.104 2819.452 Seismic
Max 21725.470 3943.447 19380.468 Positive Moment
-10816.466 Negative Moment
