Sheet 1 & 2 Imperial College of Science, Technology and Medicine Department of Civil & Environmental Engineering MSc BRIDGE MODULE - 2011/2012 Session
Bridge Abutment Design – Worked Example A bridge abutment with the configuration shown in Figure below is to be designed for the traffic of Lorries and cars to Load Model 1 of EN 1991-2. The abutment is subject to active pressure and traffic surcharge in accordance with vehicle load model in clause NA.2.34.2 of UK National Annex to BS EN 1991-2 as well as the braking load. The abutment supports a simply supported single span concrete bridge deck (beams & slab) with the following details: - Span = 20m - The characteristic vertical permanent load on abutment due to the self weight of the deck (structural elements) and finishes (non-structural elements) = 180 kN/m + 35 kN/m = 215 kN/m - Carriageway width (between kerbs) = 11m - Density of concrete = 25 kN/m3 - Concrete strength, fck = 30 Mpa - Characteristic strength of reinforcement = 500 Mpa The characteristic soil parameters are: - Density of backfill γbf = 18 kN/m3 - The angle of shearing resistance of the backfill, ϕ’bf = 35o (granular fill) - Angle of shearing resistance for clay foundation ϕ’ = 27o - The critical state angle of shearing resistance of the clay foundation, ϕ’cv = 30o - Allowable bearing pressure = 350 kN/m2
Using EN 1997-1 EN1991-2 and PD 6694-1 (for surcharge load) and Design Approach 1 calculate the following for STR/GEO Combination 1 and 2. i) Braking force ii) Active pressure iii) Horizontal traffic surcharge iv) Minimum vertical load Using the above calculated loads/forces check the abutment for: v) Sliding vi) Overturning vii) Bearing pressure Carry out structural design using EN1992 for: Dr Ali karbassi – Abutment Worked Example
2012
Sheet 1 & 2
viii) ix)
Wall stem Abutment base (toe & heel)
The following should be assumed in calculating the above. • Water table is assumed to be below the foundation level • Design/check to be based on drained condition • Traffic group gr2 only to be considered for simplicity • Wind and thermal actions to be ignored • Calculation of the load per meter run of the abutment wall to be based on average load from the carriageway width
Dr Ali karbassi – Abutment Worked Example
2012
CALCULATION SHEET Project: Section: Made by:
Work Example Abutment design Active pressure and minimum verticle force calculation AY
Ref
Calculation
EN 1991-2 Table 4.1
See Separate Sheet EN1991-2 Cl.4.4.1 (2)
Date: Sheet no:
General Details Span = 20m Lane width Deck thickness
3 m 180 mm
Characteristic backfill density, γk= Density of concrete Carriageway width Weight of concrete beam & deck on abutment Weight of non-structural elements Height of the retaining wall (from underside of base) Width of stem Thickness of base Width of the base Width of the toe (to centreline of stem) Selfweight of the stem Selfweight of the base
18 25 11 180 35 8500 800 1000 8800 2800 150 220
Actions for traffic group gr2 Maximum vertical traffic reaction, V traffic Characteristic braking force,kN Qlk =0.6 αQ1 (2Q1k) + 0.1 αq1q1kw1 L Characteristic braking force,kN/m UDL Surcharge (from PD 6694) Line Load Surcharge (from PD 6694)
kN/m3 3 kN/m m kN/m kN/m mm mm mm mm mm kN/m kN/m
145 kN/m 414 kN (for 1 lane only) 37.6 kN/m 20 Ka 660
14/03/12 1
CALCULATION SHEET Project: Section: Made by: Ref
Work Example Abutment design Sliding and Overturning resistance AY Calculation
Date: Sheet no:
14/03/12 2
Active Pressure Calculation
EN 1997-1 Annex A Table A.NA.4
EN 1997-1 Table A.3 EN1990 (Table NA.A2.4(B)) PD 6694-1 cl.4.7
Characteristic angle of Shearing Resistance, Ø'k (for backfill) γM for shearing resistance of backfill (γ Ø') Design value Ø'd sin Ø'd 1 - sin Ø'd 1 + sin Ø'd Ka (incl. γM) = (1 - sin Ø'd)/(1 + sin Ø'd) γF = γQ,sup Characteristic Backfill Density (γk) γsd;k, Model Factor Z2/2 Design Active Pressure action per metre width, H ap,d (kN/m) Distance from O Active Moment per metre width, Map,d (About O)
Characteristic 35 1 35 0.574 0.426 1.574 0.271 1.00 18 1.00 36 176 2.83 499
STR/GEO Comb.1 35 1 35 0.574 0.426 1.574 0.271 1.35 18 1.20 36 285 2.83 809
STR/GEO Comb.2 35 1.25 29.3 0.489 0.511 1.489 0.343 1.00 18 1.20 36 268 2.83 759
Characteristic 0.271 20 Ka 510 Ka 660 Ka 1170 Ka 2925 Ka 266 Ka 72 1 1 72 4.25 8.5 133 346 0.75 359 479 37.6 1.0 37.6 7.7 289.8
GEO Comb.1 0.271 72 1.35 1.2 117 4.25 8.5 180 466 0.75 485 647 37.6 1.35 50.8 7.7 391.2
GEO Comb.2 0.343 91 1.15 1.2 126 4.25 8.5 195 504 0.75 524 698 37.6 1.15 43.3 7.7 333.3
1148 978
1685 1455
1616 1457
Characteristic 180 35 150 220 585 1.00 585 18 5.60 8.5 857 1.00 857 1442 2800 6000 1638 5141 6779
GEO Comb.1 180 35 150 220 585 0.95 556 8.5 857 1.35 1157 1712 2800 6000 1556 6940 8496
GEO Comb.2 180 35 150 220 585 1.00 585 8.5 857 1.00 857 1442 2800 6000 1638 5141 6779
Horizontal Traffic Surcharge Calculation
EN 1997-1 Table A.3 PD 6694-1 cl 4.7
Ka 2 Horizontal UDL surcharge pressure σh per lane (kN/m /lane) UDL surcharge force per 3m lane, Sc1 Ka (kN/lane) = σh x 3 x z Surcharge Line Load per Lane, Sc2 Ka (kN/lane) Total Surcharge per lane = (Sc1 + Sc2) Ka = Sc3 Ka (kN/lane) Total Horizontal Surcharge = (1+1+0.5) Sc3 Ka = Sc4 Ka (kN) Horizontal Surcharge per metre width, Sc5 Ka (kN/m) Total surcharge based on Ka (kN) γF= γQ γsd;k Design traffic surcharge (per metre width), Hsc,d Distance between horizontal UDL & O Distance between Line Load & O Design UDL surcharge moment per metre width (kNm) Design Line surcharge moment per metre width (kNm) Ψ1 Design Surcharge moment per metre width (kNm) with braking force Design Surcharge moment per metre width (kNm) without braking force Characteristic braking force, Hbraking,k (kN/m) γQ Design braking force, Hbraking,d Distance between Hbraking,d & O Braking Moment per metre width, Mbraking,d (kNm) Total Moment due to Horizontal Actions Total Moment per metre width with braking force, Mhor,d (kNm) Total Moment per metre width without braking force, Mhor,d (kNm) Minimum vertical loads
EN 1997-1 Table A.NA.1 EN 1990 Table NA.A2.4(B) & (C)
EN 1990 Table NA.A2.4(B) & (C)
Weight of concrete beam & deck Weight of surfacing (50mm) Characteristic selfweight of the stem Characteristic selfweight of the base Characteristic selfweight of the superstructure,VDL,k γG,inf,DL Design selfweight VDL,inf,d (Minimum vertical load) (kN) Characteristic backfill density (γk) Width of base, X (Heel width) Height of abutment, Z(m) Backfill weight, Vsoil (kN) γG,sup,soil Design soil weight, Vsoil,d Total vertical load (per metre width) VDL,d+Vsoil,d = Vd Distance between O & Abutment Wall Distance between centre of soil & O Deck Moment about O Backfill Moment about O Minimum Moment about O due to vertical load (kNm)
CALCULATION SHEET
Project: Section: Made by: Ref
Work Example Abutment design Sliding and Overturning resistance AY Calculation
Date: Sheet no:
14/03/12 3
Sliding resistance Characteristic GEO Comb.1 GEO Comb.2
EN 1997-1 (Table A.4)
Characteristic value of the critical state shearing angle for foundations,Ø'cv,k Coefficient of friction μk=tanØ'cv,k γM applied to Ø'cv,k μd=tanØ'cv,k / γM Minimum vertical action, Vd Sliding resistance, Rd (kN) Active pressure action, Hap,d Horizontal surcharge action, Hsc,d (No Braking) Ψ1 Frequent Horizontal surcharge action, Hsc,d, freq Design braking force, Hbraking,d Total horizontal action, Hd (kN) Ratio Rd/ Hd
30 0.577 1 0.577 1442 832 176 72 0.75 54.0 37.6 268 3.1
30 0.577 1 0.577 1712 989 285 117 0.75 87.6 50.8 424 2.3
30 0.577 1.25 0.462 1442 666 268 126 0.75 94.5 43.3 406 1.6
Overturning Resistance
EN 1990 Table NA.A2 (B) & (C)
Weight of concrete beam & deck Weight of surfacing (50mm) Characteristic selfweight of the stem Characteristic selfweight of the base Characteristic selfweight of the structure,VDL,k γG,inf,DL Design selfweight VDL,inf,d (minimum vertical load, kN) Characteristic backfill density (γk) Width of base, X (Heel width) Height of abutment, Y Backfill weight, Vsoil,k γG,sup,soil Design soil weight, Vsoil,d Total vertical load (per metre width) VDL,d+Vsoil,d = Vd (kN) Distance between O & Abutment Wall Distance between centre of soil & O Deck Moment about O Backfill Moment about O Minimum Moment about O due to vertical load (kNm)
Resisting Moment Overturning Moment Ratio (Resisting/Overturning)
Characteristic GEO Comb.1 GEO Comb.2 180 180 180 35 35 35 150 150 150 220 220 220 585 585 585 1.00 0.90 1.00 585 556 585 18 5.60 8.50 8.50 8.50 857 857 857 1.00 0.90 1.00 857 771 857 1442 2800 6000 1638 5141 6779
1327 2800 6000 1556 4627 6183
1442 2800 6000 1638 5141 6779
Characteristic GEO Comb.1 GEO Comb.2 6779 6183 6779 1148 1685 1616 5.9 3.7 4.2
Project: Section: Made by: Ref
Work Example Abutment design Bearing Pressure Check - Maxium overturning moment AY Calculation
Date: Sheet no:
14/03/12 4
General Details Area of the base per metre Z
8.8 12.91
2
m 3 m
Bearing Pressure Check (with minimum overturning moment)
Weight of concrete beam & deck Weight of surfacing (50mm) Characteristic selfweight of the stem Characteristic selfweight of the base Characteristic selfweight of the structure,VDL,k EN 1991-2 Table A.NA.3
EN 1991-2 Table A.NA.3
γG,sup,DL γG,sup,surfacing Design selfweight VDL,sup,D (kN/m) Characteristic backfill density (γk) Width of base, X (Heel width) Height of abutment, Y Backfill weight, Vsoil,k γG,sup,soil Design soil weight, Vsoil,d Vertical action from traffic(per metre width),Vtraffic,k(kN/m) γF
Design traffic action, Vtraffic,d (kN/m) Total Maximum vertical load (per metre width) VDL,d+Vsoil,d+Vtraffic,d= Vd Distance between O & Abutment Wall Distance between centre of soil & O Deck Moment about O Backfill Moment about O Traffic Moment Restoring Moment (kNm) Overturning Moment (kNm) Line of application of restoring moment Distance between centreline of base to line of application of restoring moment (+ left, - right) Distance (From O) to total force applied Eccentricity of total force applied (+ left, - right) Pmax = W/A + M/Z = Pmin = W/A - M/Z =
Characteristic GEO Comb.1 GEO Comb.2 180 180 180 35 35 35 150 150 150 220 220 220 585 1.00 1.00 585 18 5.6 8.5 857 1.00 857
585 1.35 1.20 785 8.5 857 1.35 1157
585 1.00 1.00 585 8.5 857 1.00 857
145 1
145 1.35
145 1.15
145
195.8
166.8
1587 2800 6000 1638 5141 406 7185 1148 4.5 -0.13
2137 2800 6000 2197 6940 548 9685 1685 4.5 -0.13
1609 2800 6000 1638 5141 467 7246 1616 4.5 -0.10
3.80 0.60 254 107
3.74 0.66 352 134
3.50 0.90 295 71
Project: Section: Made by: Ref
Work Example Abutment design Bearing Pressure Check - Minimum overturning moment AY Calculation
Date: Sheet no:
14/03/12 5
General Details Area of the base per metre Z
2
8.8 12.91
m m3
Bearing Pressure Check (with minimum overturning moment)
EN 1991-2 Table A.NA.3
EN 1991-2 Table A.NA.3
Weight of concrete beam & deck Weight of surfacing (50mm) Characteristic selfweight of the stem Characteristic selfweight of the base Characteristic selfweight of the superstructure,VDL,k γG,sup,DL γG,sup,surfacing Design selfweight VDL,sup,D (kN/m) Characteristic backfill density (γk) Width of base, X (Heel width) Height of abutment, Y Backfill weight, Vsoil,k γG,sup,soil Design soil weight, Vsoil,d Vertical action from traffic (per metre width), Vtraffic,k (kN/m) γF
Design traffic action, Vtraffic,d (kN/m) Total Maximum vertical load (per metre width) VDL,d+Vsoil,d+Vtraffic,d= Vd Distance between O & Abutment Wall Distance between centre of soil & O Deck Moment about O Backfill Moment about O Traffic Moment Restoring Moment (kNm) Overturning Moment (kNm) Line of application of restoring moment Distance between centreline of base to line of application of restoring moment (+ left, - right) Distance (From O) to total force applied Eccentricity of total force applied (+ left, - right) Pmax = W/A + M/Z = Pmin = W/A - M/Z =
Characteristic GEO Comb.1 GEO Comb.2 180 180 180 35 35 35 150 150 150 220 220 220 585 1.00 1.00 585 18 5.6 8.5 857 1.00 857
585 1.35 1.20 785 8.5 857 1.35 1157
585 1.00 1.00 585 8.5 857 1.00 857
145
145
145
1
1.35
1.15
145
195.8
166.8
1587 2800 6000 1638 5141 406 7185 479 4.5 -0.13
2137 2800 6000 2197 6940 548 9685 876 4.5 -0.13
1609 2800 6000 1638 5141 467 7246 857 4.5 -0.10
4.23 0.17 202 159
4.12 0.28 289 197
3.97 0.43 236 129
CALCULATION SHEET Project: Section: Made by: Ref
Work Example Abutment design Stem Design AY Calculation
Date: Sheet no:
14/03/12 6
General Details Concrete grade, fck Reinforcement fyk
2 30 N/mm 2 500 N/mm
'At Rest' Pressure Calculation using Ko
EN 1997-1 (Table A.4)
EN 1997-1 (Table A.3)
Characteristic Shear Strength, Ø'k γM for shearing resistance of backfill (γØ') Design value Ø'd sin Ø'd Ko=1 - sin Ø'd γF Characteristic Backfill Density (γk) γsd;k 2 Y /2 'At rest' Pressure per metre width Distance from A Active Moment per metre width, Map,d (About A)
Characteristic GEO Comb.1 GEO Comb.2 35 35 35 1 1 1.25 35 35 29.3 0.574 0.574 0.489 0.426 0.426 0.511 1.000 1.350 1.000 18.00 18.00 18.00 1.00 1.2 1.20 28.13 28.13 28.13 215.88 349.72 310.61 2.5 2.5 2.5 540 874 777
Horizontal Traffic Surcharge Calculation
EN 1997-1 Table A.3
Ka 2 Horizontal UDL surcharge pressure σh per lane (kN/m /lane) Total UDL surcharge force per 3m lane, Sc1 Ka (kN/lane) Surcharge Line Load per Lane, Sc2 Ka (kN/lane) Total Surcharge per lane = (Sc1 + Sc2) Ka = Sc3 Ka (kN/lane) Total Horizontal Surcharge = (1+1+0.5) Sc3 Ka = Sc4 Ka (kN) Horizontal Surcharge per metre width, Sc5 Ka (kN/m) Total surcharge based on Ka (kN) γF= γQ γsd;k Design traffic surcharge (per metre width), Hsc,d Distance between horizontal UDL & A Distance between Line Load & A Design UDL surcharge moment per metre width (kNm) Design Line surcharge moment per metre width (kNm) Ψ1 Design Surcharge moment per metre width (kNm) with braking force Design Surcharge moment per metre width (kNm) without braking force Characteristic braking force, Hbraking,k (kN/m) γQ Design braking force, Hbraking,d Distance between Hbraking,d & A Braking Moment per metre width, Mbraking,d (kNm)
Characteristic GEO Comb.1 GEO Comb.2 0.271 0.271 0.343 20 Ka 510 Ka 660 Ka 1170 Ka 2925 Ka 266 Ka 72 72 91 1.00 1.35 1.15 1.0 1.2 1.2 72.1 116.7 126.0 3.3 3.3 3.3 7.5 7.5 7.5 102.1 138 149 915 915 1159 0.75 0.75 0.75 763 789 981 1017 1052 1308 37.6 37.6 37.6 1.0 1.35 1.15 37.6 50.8 43.3 7.3 7.3 7.3 275.5 371.9 316.8
Total Moment due to Horizontal Actions Total Moment per metre width with braking force, Mhor,d (kNm) Total Moment per metre width without braking force, Mhor,d (kNm)
1578 1556
2036 1927
2074 2084
Stem Design
Total Moment due to Horizontal Actions per metre width (About A) Thickness of the stem Cover Bar Diameter Effective depth, d K=M/bd2fck z= As=
Characteristic GEO Comb.1 GEO Comb.2 2036 2084 800 800 40.00 40.00 25 25 747.5 747.5 0.121 0.124 656 654 7130 7329
CALCULATION SHEET Project: Section: Made by: Ref
Work Example Abutment design Base Design AY Calculation
Date: 14/03/12 7 Sheet no:
General Details Base Design
Pmax = Pmin =
EN 1992-2
EN 1992-2
Width of pressure ∆ Rate of change of base reaction Bearing pressure at stem/toe Bearing pressure at stem/heel Toe design Design moment for toe Cover for base Bar diametre Effective depth, d K z As Heel design Design moment for toe Cover for base Bar diametre Effective depth, d K z As
Characteristic GEO Comb.1 352 197 -
GEO Comb.2 295 129
-
8.80 18 309
8.80 19 250
295
235
-
900 40 25 948 0.033 919 2252
684 40 25 948 0.025 926 1698
-
2860 40 25 948 0.106 848 7751
2917 40 25 948 0.108 846 7924
The design is based on bearing pressure. And the reinforcement summary as follow:
As required As provided Stem Reinforcement As required As provided Toe Reinforcement As required As provided Heel Reinforcement
Characteristic GEO Comb.1 7130 8378 H40 @ 150 2252 3272 H25 @ 150 7751 8378 H40 @ 150 -
GEO Comb.2 7329 8378 H40 @ 150 1698 3272 H25 @ 150 7924 8378 H40 @ 150
