Sample Abutment Diagram
Sample Abutment Diagram
Sample Abutment Diagram
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* ASTRA Pro Release 15.0 *
* TechSOFT Engineering Services *
* *
* DESIGN OF RCC ABUTMENT *
* *
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THIS RESULT CREATED ON 05.12.2020 AT 11:33:26
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USER'S DATA
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DESIGN CALCULATIONS
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STEP 1 : Approximate Sizing (dimensions)
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STEP 2 : Stability Check Weight of wall
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Weight of Base
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w3 = (L1 + L2 + L3) * d3 * γ_c
ASTRA Pro : BRIDGE_RCC_ABUTMENT , Page No : 3
= (1.95 + 0.9 + 0.75) * 1 * 24
= 86.40 kN
Distance of its centroid from Toe
D3 = (L1+L2+L3)/2 = 1.8 m
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Weight of Earth on Heel Slab
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w4 = (H - d4) * L1 * γ_b
= (5.6 - 1) * 1.95 * 18
= 161.46 kN
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Active Earth Pressure
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P1 = 0.5 * H * H * γ_b * ka
[ θ = 90° , φ = 30°, z = 0°, δ = 0
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Load from Vehicle and Approach Slab
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Equivalent height of earth for Vehicle Load Surcharge = d2 = 1.00 m
ASTRA Pro : BRIDGE_RCC_ABUTMENT , Page No : 4
D11 = (L1 / 2) + L2 + L3
= (1.95 / 2) + 0.90 + 0.75
= 2.63 m.
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V H:Long H:Trans Distance Mv Mh:Long Mh:Trans
(kN) (kN) (kN) /Height (m) (kN-m) (kN-m) (kN-m)
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1.Self Weight (w1) 56.520 D1=1.05 59.346
2.Self Weight (w2) 33.120 D2=1.50 49.680
3.Self Weight (w3) 86.400 D3=1.80 155.520
4.Weight of
Earth on Heel Slab (w4) 161.460 D4=2.63 423.833
5.Permanent Load from
Super Structure (w5) 0.000 D5=1.05 0.000
6.Active Earth Pressure (P1) 162.951 D9=2.35 383.262
7.Vertical Load for
Vehicle Load Surcharge (w8) 42.120 D11=2.63 110.565
8.Horizontal Force for
Vehicle Load Surcharge (P3) 69.836 D10=2.80 195.542
9.Seismic Force in
Longitudinal Direction
=((w1+w2+w3+w4+w5)*sc)/2
=(337.500*0.18)/2.0 = PSL 30.38 D12=H-d1 30.38*4.925
=5.60-0.68 =149.60
=4.93
10.Seismic Force in
Transverse Direction
=((w1+w2+w3+w4+w5+w8)*sc)/2
=(379.620*0.18)/2.0 = PST1 34.17D13=B 34.17*7.3
=7.3 =249.41
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Sum of Items in V1= H1:Long H1:Trans MV1= MH1:Long MH1:Trans
Span Unloaded Condition 379.62 263.16 34.17 798.94 728.40 249.410
Design Values V1= H1= MV1= MH1
379.62 263.16 798.94 728.40
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11.Horizontal
Break Force (P2) 3.425 D7=4.93 16.866
12.Vehicle
Braking Force (w7) 1.387 D8=1.05 1.456
13.Vehicle Load from
Super Structure (w6) 130.000 D6=1.05 136.500
14.Additional Seismic Force D14
Transverse Direction = PST2 =H+d3
=((w6+w7)*sc)/2.0 =5.60 + 0.15
=((130.00+1.39)*0.18)/2.0 =5.75 11.82*5.75
=11.82 67.99
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Sum of Items in V2= H2:Long H2:Trans MV2= MH2:Long MH2:Trans
Span Loaded Condition 511.01 266.59 45.99 936.90 745.27 317.403
Design Values V2= H2= MV2= MH2
511.01 266.59 936.90 745.27
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STEP 3 : Check for Stability against Overturning
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ASTRA Pro : BRIDGE_RCC_ABUTMENT , Page No : 5
CASE I : Span Unloaded Condition
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Overturning Moment about toe = MH1 = 728.400
Restoring Moment about toe = MV1 = 798.944
Factor of Safety against overturning = 798.94 / 728.40 = 1.097 < 2.0, NOT OK
Location of Resultant for toe = Xo = (MV1 - MH1)/V1
= (798.944 - 728.400)/379.620
= 0.186
Maximum permissible Eccentricity = emax = (L1 + L2 + L3)/6.0
= (1.95 + 0.9 + 0.75)/6.0
= 0.6000
Eccentricity of Resultant = e2 = (L1 + L2 + L3)/2 - Xo
= (1.95 + 0.9 + 0.75)/2 - 0.19
= 1.614 > 0.600(emax), NOT OK
Increase the length of base of wall on Earth Retaining Side,
more than present length of 1.95 m (L1)
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CASE II : Span Loaded Condition
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Overturning Moment about toe = MH2 = 745.266 kN-m.
Restoring Moment about toe = MV2 = 936.900 kN-m.
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STEP 4 : Check for Stresses at Base For Span Loaded Condition
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STEP 5 : Check for Sliding
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Longitudinal Sliding Force = H2:Long = 266.587 kN
Force resisting Sliding = µ * V2 = 0.60 * 511.01 = 306.604 = FF
Factor of Safety against Sliding = FF/H2:Long = 306.604/266.587 = 1.150 < 1.5 , NOT OK
Shear key will be required.
Transverse Sliding Force = H2:Trans = 45.991 kN
ASTRA Pro : BRIDGE_RCC_ABUTMENT , Page No : 6
Force resisting Sliding = µ * V2 = 0.60 * 511.01 = 306.604 = FF
Factor of Safety against Sliding = FF/H2:Trans = 306.604/45.991 = 6.667 > 1.5 , OK
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STEP 6 : Reinforcement Steel Bars
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Design of Base Slab at Front Toe for Steel requirements.
ON BASE :
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Area of Steel required at bottom Base slab at Toe
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Mu = 0.87 * f_y * Ast * [d - (f_y * Ast)/(f_ck * b)]
26.09 * 10^6 = 0.87 * 415.000 * Ast * [950.00 - (415.00 * Ast)/(25.00 * 1000.00)]
Ast * Ast - 57228.92 * Ast + 4.35*10^6 = 0
Ast = (57228.92 ± √(57228.92*57228.92 - 4*4.354*10^6))/2
= (57228.92 ± 57076.56)/2
= 57152.74, 76.18
Provided T12 bars @ 200 mm c/c at bottom of Base Slab at Toe Marked as (4) in the Drawing
Applied Shear Stress τ_v = Vu/b*d = 171.415 * 1000/(1000.00*950.00) = 0.180 <= 0.340 , OK
Distribution Steel = 0.12/100 * 1000 * 0.95 = 1140.00 sq.mm.
Provide T10 @ 90 mm c/c Marked as (5) in the Drawing
Steel Area Provided = 942.478 sq.mm
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STEP 7 : Design of Base Slab at Backfill Heel Side for Steel Reinforcement
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Upward Pressure varies from Pr3 = 533.77 to Pr5 = -195.17
downward Pressure is Earth Load + Surcharge + Self Weight
ASTRA Pro : BRIDGE_RCC_ABUTMENT , Page No : 7
Pr6 = (H-d4)*γ_b + h2 * γ_b + d3*γ_c + d4*γ_c
= (5.600-1.00)*18.00 + 1.00 * 18.00 + 0.15*24.00 + 1.000*24.000
= 128.40
Here downward pressure Pr6 = 128.40 is more than Pr4 = 365.21 and Pr5 = -195.17
So, tension reinforcement steel will be required at the top
Design Shear Force
Vu = Shear Force Factor * (Pr6 * L1 - 0.5 * Pr4 * L1 - 0.5 * Pr5 * L1)
= 1.50 * (128.40 * 1.95 - 0.5 * 365.213 * 1.950 - 0.5 * -195.174 * 1.950)
= 126.89 kN
Design Bending Moment = Mu
Mu = Bending Moment Factor * ((Pr6 * L1 * L1 * 0.5)
- (0.5 * Pr4 * L1 * L1 * 0.33) - 0.5 * Pr5 * L1 * L1 * 0.67))
= 1.50 * ((128.40 * 1.950 * 1.950 * 0.5)
- (0.5 * 365.213 * 1.950 * 1.950 * 0.33)
- (0.5 * 128.400 * 1.950 * 1.950 * 0.67))
= 395.40 kN-m
Effective Depth of Base Slab at Heel = √((Mu * 10^6)/(0.138*f_ck*b))
= √((395.40 * 10^6)/(0.138*25.00*1000.00))
= 338.54 mm < 950.00
Area of Steel required at top of base slab at Heel
Mu = 0.87 * σ_st * Ast * (d-((f_y*Ast)/(f_ck*b))
395.40*10^6 = 0.87 * 415.00 * Ast * (950.00-((415.00*Ast)/(25*1000))
Ast*Ast - 57228.92*Ast + 342997.50*10^6 = 0
Ast = 56051.93 and 1176.99 sq.mm.
Provide T16 bars @200 mm c/c at Top of bar slab at Heel. Marked as (6) in the Drawing
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STEP 8 : Design of Wall Reinforcement
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Allowable Shear Stress of M25 Concrete = τ_c = 0.50 N/sq.mm Refer to TABLE 1
Applied Shear Stress = τ_v = Vu * 1000 / (b * (t * 1000 - cover))
= 126.887*1000 / (1000.000 * (0.900 * 1000 - 50.000))
= 0.134 <= τ_c , OK
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