abutment worked example

Sheet 1 & 2

Dr Ali karbassi – Abutment Worked Example 2012

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:

Sheet 1 & 2

Dr Ali karbassi – Abutment Worked Example 2012

viii) Wall stem ix) 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

CALCULATION SHEETProject: Work ExampleSection: Abutment design

Active pressure and minimum verticle force calculation Date: 14/03/12Made by: AY Sheet no: 1Ref Calculation

General DetailsSpan = 20m

EN 1991-2 Table 4.1 Lane width 3 mDeck thickness 180 mm

Characteristic backfill density, γk= 18 kN/m3

Density of concrete 25 kN/m3

Carriageway width 11 mWeight of concrete beam & deck on abutment 180 kN/mWeight of non-structural elements 35 kN/mHeight of the retaining wall (from underside of base) 8500 mmWidth of stem 800 mmThickness of base 1000 mmWidth of the base 8800 mmWidth of the toe (to centreline of stem) 2800 mmSelfweight of the stem 150 kN/mSelfweight of the base 220 kN/m

Actions for traffic group gr2See Separate Sheet Maximum vertical traffic reaction, Vtraffic 145 kN/m

EN1991-2 Cl.4.4.1 (2)Characteristic braking force,kN Qlk =0.6 αQ1 (2Q1k) + 0.1 αq1q1kw1 L 414 kN (for 1 lane only)Characteristic braking force,kN/m 37.6 kN/mUDL Surcharge (from PD 6694) 20 KaLine Load Surcharge (from PD 6694) 660


Sliding and Overturning resistance Date: 14/03/12Made by: AY Sheet no: 2Ref Calculation

Active Pressure Calculation

STR/GEO Comb.1 STR/GEO Comb.2Characteristic angle of Shearing Resistance, Ø'k (for backfill) 35 35

EN 1997-1 Annex A γM for shearing resistance of backfill (γØ') 1 1.25Table A.NA.4 Design value Ø'd 35 29.3

sin Ø'd 0.574 0.4891 - sin Ø'd 0.426 0.5111 + sin Ø'd 1.574 1.489Ka (incl. γM) = (1 - sin Ø'd)/(1 + sin Ø'd) 0.271 0.343

EN 1997-1 Table A.3 γF = γQ,sup 1.35 1.00EN1990 (Table NA.A2.4(B)) Characteristic Backfill Density (γk) 18 18PD 6694-1 cl.4.7 γsd;k, Model Factor 1.20 1.20

Z2/2 36 36Design Active Pressure action per metre width, Hap,d (kN/m) 285 268Distance from O 2.83 2.83Active Moment per metre width, Map,d (About O) 809 759

Horizontal Traffic Surcharge Calculation

GEO Comb.1 GEO Comb.2Ka 0.271 0.343Horizontal UDL surcharge pressure σh per lane (kN/m2/lane) 20 Ka - -UDL surcharge force per 3m lane, Sc1 Ka (kN/lane) = σh x 3 x z 510 Ka - -Surcharge Line Load per Lane, Sc2 Ka (kN/lane) 660 Ka - -Total Surcharge per lane = (Sc1 + Sc2) Ka = Sc3 Ka (kN/lane) 1170 Ka - -Total Horizontal Surcharge = (1+1+0.5) Sc3 Ka = Sc4 Ka (kN) 2925 Ka - -Horizontal Surcharge per metre width, Sc5 Ka (kN/m) 266 Ka - -Total surcharge based on Ka (kN) 72 91

EN 1997-1 Table A.3 γF= γQ 1.35 1.15PD 6694-1 cl 4.7 γsd;k 1.2 1.2

Design traffic surcharge (per metre width), Hsc,d 117 126Distance between horizontal UDL & O 4.25 4.25Distance between Line Load & O 8.5 8.5Design UDL surcharge moment per metre width (kNm) 180 195Design Line surcharge moment per metre width (kNm) 466 504Ψ1 0.75 0.75Design Surcharge moment per metre width (kNm) with braking force 485 524Design Surcharge moment per metre width (kNm) without braking force 647 698Characteristic braking force, Hbraking,k (kN/m) 37.6 37.6γQ 1.35 1.15Design braking force, Hbraking,d 50.8 43.3Distance between Hbraking,d & O 7.7 7.7Braking Moment per metre width, Mbraking,d (kNm) 391.2 333.3

Total Moment due to Horizontal Actions

Total Moment per metre width with braking force, Mhor,d (kNm) 1685 1616Total Moment per metre width without braking force, Mhor,d (kNm) 1455 1457

Minimum vertical loads

GEO Comb.1 GEO Comb.2Weight of concrete beam & deck 180 180Weight of surfacing (50mm) 35 35Characteristic selfweight of the stem 150 150Characteristic selfweight of the base 220 220Characteristic selfweight of the superstructure,VDL,k 585 585

EN 1997-1 Table A.NA.1 γG,inf,DL 0.95 1.00EN 1990 Table NA.A2.4(B) & (C) Design selfweight VDL,inf,d (Minimum vertical load) (kN) 556 585

Characteristic backfill density (γk) - -Width of base, X (Heel width) - -Height of abutment, Z(m) 8.5 8.5Backfill weight, Vsoil (kN) 857 857

EN 1990 Table NA.A2.4(B) & (C) γG,sup,soil 1.35 1.00Design soil weight, Vsoil,d 1157 857Total vertical load (per metre width) VDL,d+Vsoil,d = Vd 1712 1442Distance between O & Abutment Wall 2800 2800Distance between centre of soil & O 6000 6000Deck Moment about O 1556 1638Backfill Moment about O 6940 5141Minimum Moment about O due to vertical load (kNm) 8496 6779

280060001638

67795141

35

479

1148

Characteristic

7.7289.8

37.61.0

37.6

3590.75

8.5857

1442

180

1.00857

150220

1.00585

58518

5.60

978

72

346

11

724.25

1338.5

176

Characteristic0.271

499

1.5740.2711.0018

1.0036

2.83

0.426

Characteristic351

350.574

CALCULATION SHEET

Project: Work ExampleSection: Abutment design

Sliding and Overturning resistance Date: 14/03/12Made by: AY Sheet no: 3Ref Calculation

Sliding resistance

GEO Comb.1 GEO Comb.2Characteristic value of the critical state shearing angle for foundations,Ø'cv,k 30 30Coefficient of friction μk=tanØ'cv,k 0.577 0.577

EN 1997-1 (Table A.4) γM applied to Ø'cv,k 1 1.25 μd=tanØ'cv,k / γM 0.577 0.462Minimum vertical action, Vd 1712 1442Sliding resistance, Rd (kN) 989 666Active pressure action, Hap,d 285 268Horizontal surcharge action, Hsc,d (No Braking) 117 126Ψ1 0.75 0.75Frequent Horizontal surcharge action, Hsc,d, freq 87.6 94.5Design braking force, Hbraking,d 50.8 43.3Total horizontal action, Hd (kN) 424 406Ratio Rd/ Hd 2.3 1.6

Overturning Resistance

GEO Comb.1 GEO Comb.2Weight of concrete beam & deck 180 180Weight of surfacing (50mm) 35 35Characteristic selfweight of the stem 150 150Characteristic selfweight of the base 220 220Characteristic selfweight of the structure,VDL,k 585 585γG,inf,DL 0.90 1.00Design selfweight VDL,inf,d (minimum vertical load, kN) 556 585Characteristic backfill density (γk) - -Width of base, X (Heel width) - -Height of abutment, Y 8.50 8.50Backfill weight, Vsoil,k 857 857

EN 1990 Table NA.A2 (B) & (C) γG,sup,soil 0.90 1.00Design soil weight, Vsoil,d 771 857Total vertical load (per metre width) VDL,d+Vsoil,d = Vd (kN) 1327 1442Distance between O & Abutment Wall 2800 2800Distance between centre of soil & O 6000 6000Deck Moment about O 1556 1638Backfill Moment about O 4627 5141Minimum Moment about O due to vertical load (kNm) 6183 6779

GEO Comb.1 GEO Comb.2Resisting Moment 6183 6779Overturning Moment 1685 1616Ratio (Resisting/Overturning) 3.7 4.2

1

37.6

Characteristic67791148

1502205851.0058518

5.608.508571.00857

5.9

Characteristic

300.577

3.1

0.5771442832176

54.0

720.75

268

Characteristic18035

1442

6779

2800600016385141


Bearing Pressure Check - Maxium overturning moment Date: 14/03/12Made by: AY Sheet no: 4Ref Calculation

General Details

Area of the base per metre 8.8 m2

Z 12.91 m3

Bearing Pressure Check (with minimum overturning moment)

GEO Comb.1 GEO Comb.2Weight of concrete beam & deck 180 180Weight of surfacing (50mm) 35 35Characteristic selfweight of the stem 150 150Characteristic selfweight of the base 220 220Characteristic selfweight of the structure,VDL,k

585 585EN 1991-2 Table A.NA.3 γG,sup,DL 1.35 1.00

γG,sup,surfacing 1.20 1.00Design selfweight VDL,sup,D (kN/m) 785 585Characteristic backfill density (γk) - -Width of base, X (Heel width) - -Height of abutment, Y 8.5 8.5Backfill weight, Vsoil,k 857 857

EN 1991-2 Table A.NA.3 γG,sup,soil 1.35 1.00Design soil weight, Vsoil,d 1157 857Vertical action from traffic(per metre width),Vtraffic,k(kN/m) 145 145γF 1.35 1.15

Design traffic action, Vtraffic,d (kN/m) 195.8 166.8Total Maximum vertical load (per metre width) VDL,d+Vsoil,d+Vtraffic,d= Vd 2137 1609Distance between O & Abutment Wall 2800 2800Distance between centre of soil & O 6000 6000Deck Moment about O 2197 1638Backfill Moment about O 6940 5141Traffic Moment 548 467Restoring Moment (kNm) 9685 7246Overturning Moment (kNm) 1685 1616Line of application of restoring moment 4.5 4.5Distance between centreline of base to line of application of restoring moment (+ left, - right)

-0.13 -0.10

Distance (From O) to total force applied 3.74 3.50Eccentricity of total force applied (+ left, - right) 0.66 0.90Pmax = W/A + M/Z = 352 295Pmin = W/A - M/Z = 134 71

-0.13

3.800.60254107

16385141406718511484.5

145

158728006000

8.58571.00857

1451

5851.001.00585185.6

Characteristic18035

150220


Bearing Pressure Check - Minimum overturning moment Date: 14/03/12Made by: AY Sheet no: 5Ref Calculation

General Details

Area of the base per metre 8.8 m2

Z 12.91 m3

Bearing Pressure Check (with minimum overturning moment)

GEO Comb.1 GEO Comb.2Weight of concrete beam & deck 180 180Weight of surfacing (50mm) 35 35Characteristic selfweight of the stem 150 150Characteristic selfweight of the base 220 220Characteristic selfweight of the superstructure,VDL,k 585 585

EN 1991-2 Table A.NA.3 γG,sup,DL 1.35 1.00γG,sup,surfacing 1.20 1.00Design selfweight VDL,sup,D (kN/m) 785 585Characteristic backfill density (γk) - -Width of base, X (Heel width) - -Height of abutment, Y 8.5 8.5Backfill weight, Vsoil,k 857 857

EN 1991-2 Table A.NA.3 γG,sup,soil 1.35 1.00Design soil weight, Vsoil,d 1157 857Vertical action from traffic (per metre width), Vtraffic,k (kN/m) 145 145γF 1.35 1.15

Design traffic action, Vtraffic,d (kN/m) 195.8 166.8Total Maximum vertical load (per metre width) VDL,d+Vsoil,d+Vtraffic,d= Vd 2137 1609Distance between O & Abutment Wall 2800 2800Distance between centre of soil & O 6000 6000Deck Moment about O 2197 1638Backfill Moment about O 6940 5141Traffic Moment 548 467Restoring Moment (kNm) 9685 7246Overturning Moment (kNm) 876 857Line of application of restoring moment 4.5 4.5Distance between centreline of base to line of application of restoring moment (+ left, - right)

-0.13 -0.10

Distance (From O) to total force applied 4.12 3.97Eccentricity of total force applied (+ left, - right) 0.28 0.43Pmax = W/A + M/Z = 289 236Pmin = W/A - M/Z = 197 129

-0.13

4.230.17202159

16385141406

71854794.5

145

158728006000

8.58571.00857

1451

5851.001.00585185.6

Characteristic18035

150220


Stem Design Date: 14/03/12Made by: AY Sheet no: 6Ref Calculation

General Details

Concrete grade, fck 30 N/mm2

Reinforcement fyk 500 N/mm2

'At Rest' Pressure Calculation using Ko

GEO Comb.1 GEO Comb.2Characteristic Shear Strength, Ø'k 35 35

EN 1997-1 (Table A.4) γM for shearing resistance of backfill (γØ') 1 1.25Design value Ø'd 35 29.3sin Ø'd 0.574 0.489Ko=1 - sin Ø'd 0.426 0.511

EN 1997-1 (Table A.3) γF 1.350 1.000Characteristic Backfill Density (γk) 18.00 18.00γsd;k 1.2 1.20Y2/2 28.13 28.13'At rest' Pressure per metre width 349.72 310.61Distance from A 2.5 2.5Active Moment per metre width, Map,d (About A) 874 777

Horizontal Traffic Surcharge Calculation

GEO Comb.1 GEO Comb.2Ka 0.271 0.343Horizontal UDL surcharge pressure σh per lane (kN/m2/lane) 20 Ka - -Total UDL surcharge force per 3m lane, Sc1 Ka (kN/lane) 510 Ka - -Surcharge Line Load per Lane, Sc2 Ka (kN/lane) 660 Ka - -Total Surcharge per lane = (Sc1 + Sc2) Ka = Sc3 Ka (kN/lane) 1170 Ka - -Total Horizontal Surcharge = (1+1+0.5) Sc3 Ka = Sc4 Ka (kN) 2925 Ka - -Horizontal Surcharge per metre width, Sc5 Ka (kN/m) 266 Ka - -Total surcharge based on Ka (kN) 72 91γF= γQ 1.35 1.15γsd;k 1.2 1.2Design traffic surcharge (per metre width), Hsc,d 116.7 126.0Distance between horizontal UDL & A 3.3 3.3Distance between Line Load & A 7.5 7.5Design UDL surcharge moment per metre width (kNm) 138 149Design Line surcharge moment per metre width (kNm) 915 1159Ψ1 0.75 0.75

EN 1997-1 Table A.3 Design Surcharge moment per metre width (kNm) with braking force 789 981Design Surcharge moment per metre width (kNm) without braking force 1052 1308Characteristic braking force, Hbraking,k (kN/m) 37.6 37.6γQ 1.35 1.15Design braking force, Hbraking,d 50.8 43.3Distance between Hbraking,d & A 7.3 7.3Braking Moment per metre width, Mbraking,d (kNm) 371.9 316.8

Total Moment due to Horizontal Actions

Total Moment per metre width with braking force, Mhor,d (kNm) 2036 2074Total Moment per metre width without braking force, Mhor,d (kNm) 1927 2084

Stem Design

GEO Comb.1 GEO Comb.2Total Moment due to Horizontal Actions per metre width (About A) 2036 2084Thickness of the stem 800 800Cover 40.00 40.00Bar Diameter 25 25Effective depth, d 747.5 747.5K=M/bd2fck 0.121 0.124z= 656 654As= 7130 7329

2.5540

763

1.037.6

0.75

101737.6

721.00

7.5102.1915

Characteristic0.271

Characteristic-

---

--

-

Characteristic35135

1.0028.13215.88

0.5740.4261.00018.00

-

1.072.13.3

15781556

275.57.3


Base Design Date: 14/03/12Made by: AY Sheet no: 7Ref Calculation

General Details

Base Design

GEO Comb.1 GEO Comb.2Pmax = 352 295Pmin = 197 129Width of pressure ∆ 8.80 8.80Rate of change of base reaction 18 19Bearing pressure at stem/toe 309 250Bearing pressure at stem/heel 295 235

Design moment for toe 900 684Cover for base 40 40Bar diametre 25 25Effective depth, d 948 948

EN 1992-2 K 0.033 0.025z 919 926As 2252 1698

Design moment for toe 2860 2917Cover for base 40 40Bar diametre 25 25Effective depth, d 948 948

EN 1992-2 K 0.106 0.108z 848 846As 7751 7924

The design is based on bearing pressure. And the reinforcement summary as follow:

GEO Comb.1 GEO Comb.2As required 7130 7329As provided 8378 8378Stem Reinforcement H40 @ 150 H40 @ 150As required 2252 1698As provided 3272 3272Toe Reinforcement H25 @ 150 H25 @ 150As required 7751 7924As provided 8378 8378Heel Reinforcement H40 @ 150 H40 @ 150

-

Characteristic

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-

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-

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Toe design

Heel design

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Characteristic---

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abutment worked example

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