Abutment Worked Example

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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/m

3

- Concrete strength, f

ck

= 30 Mpa

- Characteristic strength of reinforcement = 500 Mpa

The characteristic soil parameters are:

- Density of backfill γ

bf

= 18 kN/m

3

- The angle of shearing resistance of the backfill, ϕ’

bf

= 35

o

(granular fill)

- Angle of shearing resistance for clay foundation ϕ’ = 27

o

- The critical state angle of shearing resistance of the clay foundation, ϕ

’

cv

= 30

o

- Allowable bearing pressure = 350 kN/m

2

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

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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

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CALCULATION SHEET

Project: Work Example

Section: Abutment design

Active pressure and minimum verticle force calculation Date: 14/03/12

Made by: AY Sheet no: 1

Ref Calculation

General Details

Span = 20m

EN 1991-2 Table 4.1 Lane width 3 m

Deck thickness 180 mm

Characteristic backfill density, γk= 18 kN/m3

Density of concrete 25 kN/m3

Carriageway width 11 m

Weight of concrete beam & deck on abutment 180 kN/m

Weight of non-structural elements 35 kN/m

Height of the retaining wall (from underside of base) 8500 mm

Width of stem 800 mm

Thickness of base 1000 mm

Width of the base 8800 mm

Width of the toe (to centreline of stem) 2800 mm

Selfweight of the stem 150 kN/m

Selfweight of the base 220 kN/m

Actions for traffic group gr2

See Separate Sheet Maximum vertical traffic reaction, Vtraffic 145 kN/m

EN1991-2 Cl.4.4.1 (2)

Characteristic braking force,kN

Qlk =0.6αQ1 (2Q1k)+ 0.1 αq1q1kw1 L 414 kN (for 1 lane only)

Characteristic braking force,kN/m 37.6 kN/m

UDL Surcharge (from PD 6694) 20 Ka

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Sliding and Overturning resistance Date: 14/03/12

Active Pressure Calculation

STR/GEO Comb.1 STR/GEO Comb.2

Characteristic angle of Shearing Resistance, Ø'k (for backfill) 35 35

EN 1997-1 Annex A γM for shearing resistance of backfill (γØ') 1 1.25

Table A.NA.4 Design value Ø'd 35 29.3

sin Ø'd 0.574 0.489

1 - sin Ø'd 0.426 0.511

1 + sin Ø'd 1.574 1.489

Ka (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 1.00

EN1990 (Table NA.A2.4(B)) Characteristic Backfill Density (γk) 18 18

PD 6694-1 cl.4.7 γsd;k, Model Factor 1.20 1.20

Z2/2 36 36

Design Active Pressure action per metre width, Hap,d (kN/m) 285 268

Distance from O 2.83 2.83

Active Moment per metre width, Map,d (About O) 809 759

Horizontal Traffic Surcharge Calculation

GEO Comb.1 GEO Comb.2

Ka 0.271 0.343

Horizontal UDL surcharge pressure σh per lane (kN/m

2_/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 1.15

PD 6694-1 cl 4.7 γsd;k 1.2 1.2

Design traffic surcharge (per metre width), Hsc,d 117 126

Distance between horizontal UDL & O 4.25 4.25

Distance between Line Load & O 8.5 8.5

Design UDL surcharge moment per metre width (kNm) 180 195

Design Line surcharge moment per metre width (kNm) 466 504

Ψ1 0.75 0.75

Design Surcharge moment per metre width (kNm) with braking force 485 524 Design Surcharge moment per metre width (kNm) without braking force 647 698

Characteristic braking force, Hbraking,k (kN/m) 37.6 37.6

γQ 1.35 1.15

Design braking force, Hbraking,d 50.8 43.3

Distance between Hbraking,d & O 7.7 7.7

Braking 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 1616

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

Minimum vertical loads

Weight of concrete beam & deck 180 180

Weight of surfacing (50mm) 35 35

Characteristic selfweight of the stem 150 150

Characteristic selfweight of the base 220 220

Characteristic selfweight of the superstructure,VDL,k 585 585

EN 1997-1 Table A.NA.1 γG,inf,DL 0.95 1.00

EN 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 8.5

Backfill weight, Vsoil (kN) 857 857

EN 1990 Table NA.A2.4(B) & (C) γG,sup,soil 1.35 1.00

Design soil weight, Vsoil,d 1157 857

Total vertical load (per metre width) VDL,d+Vsoil,d = Vd 1712 1442

Distance between O & Abutment Wall 2800 2800

Distance between centre of soil & O 6000 6000

Deck Moment about O 1556 1638

Backfill Moment about O 6940 5141

Minimum Moment about O due to vertical load (kNm) 8496 6779

2800 6000 1638 6779 5141 35 479 1148 Characteristic 7.7 289.8 37.6 1.0 37.6 359 0.75 8.5 857 1442 180 1.00 857 150 220 1.00 585 585 18 5.60 978 72 346 1 1 72 4.25 133 8.5 176 Characteristic 0.271 499 1.574 0.271 1.00 18 1.00 36 2.83 0.426 Characteristic 35 1 35 0.574

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CALCULATION SHEET

Sliding and Overturning resistance Date: 14/03/12

Sliding resistance

GEO Comb.1 GEO Comb.2 Characteristic value of the critical state shearing angle for

foundations,Ø'cv,k 30 30

Coefficient 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 0.462

Minimum vertical action, Vd 1712 1442

Sliding resistance, Rd (kN) 989 666

Active pressure action, Hap,d 285 268

Horizontal surcharge action, Hsc,d (No Braking) 117 126

Ψ1 0.75 0.75

Frequent Horizontal surcharge action, Hsc,d, freq 87.6 94.5

Design braking force, Hbraking,d 50.8 43.3

Total horizontal action, Hd (kN) 424 406

Ratio Rd/ Hd 2.3 1.6

Overturning Resistance

Weight of concrete beam & deck 180 180

Weight of surfacing (50mm) 35 35

Characteristic selfweight of the stem 150 150

Characteristic selfweight of the base 220 220

Characteristic selfweight of the structure,VDL,k 585 585

γG,inf,DL 0.90 1.00

Design selfweight VDL,inf,d (minimum vertical load, kN) 556 585

Characteristic backfill density (γk) -

-Width of base, X (Heel width) -

-Height of abutment, Y 8.50 8.50

Backfill weight, Vsoil,k 857 857

EN 1990 Table NA.A2 (B) & (C) γG,sup,soil 0.90 1.00

Design soil weight, Vsoil,d 771 857

Total vertical load (per metre width)

VDL,d+Vsoil,d = Vd (kN) 1327 1442

Distance between O & Abutment Wall 2800 2800

Distance between centre of soil & O 6000 6000

Deck Moment about O 1556 1638

Backfill Moment about O 4627 5141

Minimum Moment about O due to vertical load (kNm) 6183 6779

Resisting Moment 6183 6779 Overturning Moment 1685 1616 Ratio (Resisting/Overturning) 3.7 4.2 1 37.6 Characteristic 6779 1148 150 220 585 1.00 585 18 5.60 8.50 857 1.00 857 5.9 Characteristic 30 0.577 3.1 0.577 1442 832 176 54.0 72 0.75 268 Characteristic 180 35 1442 6779 2800 6000 1638 5141

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Project:

Work Example

Section:

Abutment design

Bearing Pressure Check - Maxium overturning moment

Date:

14/03/12

Made by:

AY

Sheet no:

4 Ref

Calculation

General Details

Area of the base per metre

8.8 m

2

Z

12.91 m

3

Bearing Pressure Check (with minimum overturning moment)

GEO Comb.1 GEO Comb.2

Weight of concrete beam & deck

180

180 Weight of surfacing (50mm)

35

35 Characteristic selfweight of the stem

150

150 Characteristic selfweight of the base

220

220 Characteristic selfweight of the structure,V

DL,k

585

585 EN 1991-2 Table A.NA.3

γ

G,sup,DL

1.35

1.00 γ

G,sup,surfacing

1.20

1.00 Design selfweight V

DL,sup,D

(kN/m)

785

585 Characteristic backfill density (γ

k

)

-

-Width of base, X (Heel width)

-

-Height of abutment, Y

8.5

8.5 Backfill weight, Vsoil,k

857

857 EN 1991-2 Table A.NA.3

γG,sup,soil

1.35

1.00 Design soil weight, Vsoil,d

1157

857 Vertical action from traffic(per metre

width),V

traffic,k

(kN/m)

145

γF

_1.35

_1.15

Design traffic action, V

traffic,d

(kN/m)

195.8

166.8 Total Maximum vertical load (per metre width)

V

DL,d

+V

soil,d

+V

traffic,d

= V

d

2137

1609

Distance between O & Abutment Wall

2800

Distance between centre of soil & O

6000

Deck Moment about O

2197

1638

Backfill Moment about O

6940

5141

Traffic Moment

548

467 Restoring Moment (kNm)

9685

7246

Overturning Moment (kNm)

1685

1616

Line of application of restoring moment

4.5

4.5 Distance 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

3.50 Eccentricity of total force applied (+ left, - right)

0.66

0.90 Pmax = W/A + M/Z =

352

295 Pmin = W/A - M/Z =

134

71 -0.13

3.80

0.60

254

107 1638

5141

406 7185

1148

4.5

145 1587

2800

6000

8.5

857

1.00

857

145

1

585

1.00

585

18

5.6 Characteristic

180

35

150

220

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Project:

Work Example

Section:

Abutment design

Bearing Pressure Check - Minimum overturning moment

Date:

14/03/12

Made by:

AY

Sheet no:

5 Ref

Calculation

General Details

Area of the base per metre

8.8 m

2

Z

12.91 m

3

Bearing Pressure Check (with minimum overturning moment)

GEO Comb.1 GEO Comb.2

Weight of concrete beam & deck

180

180 Weight of surfacing (50mm)

35

35 Characteristic selfweight of the stem

150

150 Characteristic selfweight of the base

220

220 Characteristic selfweight of the

superstructure,V

DL,k

585

585 EN 1991-2 Table A.NA.3

γ

G,sup,DL

1.35

1.00 γ

G,sup,surfacing

1.20

1.00 Design selfweight V

DL,sup,D

(kN/m)

785

585 Characteristic backfill density (γ

k

)

-

-Width of base, X (Heel width)

-

-Height of abutment, Y

8.5

8.5 Backfill weight, V

soil,k

857

857 EN 1991-2 Table A.NA.3

γ

G,sup,soil

1.35

1.00 Design soil weight, V

soil,d

1157

857 Vertical action from traffic (per metre width),

V

traffic,k

(kN/m)

145

γF

_1.35

_1.15

Design traffic action, V

traffic,d

(kN/m)

195.8

166.8 Total Maximum vertical load (per metre width)

V

DL,d

+V

soil,d

+V

traffic,d

= V

d

2137

1609

Distance between O & Abutment Wall

2800

Distance between centre of soil & O

6000

Deck Moment about O

2197

1638

Backfill Moment about O

6940

5141

Traffic Moment

548

467 Restoring Moment (kNm)

9685

7246

Overturning Moment (kNm)

876

857 Line of application of restoring moment

4.5

4.5 Distance 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

3.97 Eccentricity of total force applied (+ left, - right)

0.28

0.43 Pmax = W/A + M/Z =

289

236 Pmin = W/A - M/Z =

197

129 -0.13

4.23

0.17

202

159 1638

5141

406 7185

479

4.5

145 1587

2800

6000

8.5

857

1.00

857

145

1

585

1.00

585

18

5.6 Characteristic

180

35

150

220

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Stem Design Date: 14/03/12

Ref Calculation General Details Concrete grade, fck 30 N/mm 2 Reinforcement fyk 500 N/mm 2

'At Rest' Pressure Calculation using Ko

Characteristic Shear Strength, Ø'k 35 35

EN 1997-1 (Table A.4) γM for shearing resistance of backfill (γØ') 1 1.25

Design value Ø'd 35 29.3

sin Ø'd 0.574 0.489

Ko=1 - sin Ø'd 0.426 0.511

EN 1997-1 (Table A.3) γF 1.350 1.000

Characteristic Backfill Density (γk) 18.00 18.00

γsd;k 1.2 1.20

Y2/2 28.13 28.13

'At rest' Pressure per metre width 349.72 310.61

Distance from A 2.5 2.5

Active Moment per metre width, Map,d (About A) 874 777

Horizontal Traffic Surcharge Calculation

Ka 0.271 0.343

Horizontal UDL surcharge pressure σh per lane (kN/m 2

/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 91

γF= γQ 1.35 1.15

γsd;k 1.2 1.2

Design traffic surcharge (per metre width), Hsc,d 116.7 126.0

Distance between horizontal UDL & A 3.3 3.3

Distance between Line Load & A 7.5 7.5

Design UDL surcharge moment per metre width (kNm) 138 149

Design Line surcharge moment per metre width (kNm) 915 1159

Ψ1 0.75 0.75

EN 1997-1 Table A.3 Design Surcharge moment per metre width (kNm) with braking force 789 981

Design Surcharge moment per metre width (kNm) without braking force 1052 1308

Characteristic braking force, Hbraking,k (kN/m) 37.6 37.6

γQ 1.35 1.15

Design braking force, Hbraking,d 50.8 43.3

Distance between Hbraking,d & A 7.3 7.3

Braking 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 2074

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

Stem Design

Total Moment due to Horizontal Actions per metre width (About A) 2036 2084

Thickness of the stem 800 800

Cover 40.00 40.00 Bar Diameter 25 25 Effective depth, d 747.5 747.5 K=M/bd2fck 0.121 0.124 z= 656 654 As= 7130 7329 2.5 540 763 1.0 37.6 0.75 1017 37.6 72 1.00 7.5 102.1 915 Characteristic 0.271 Characteristic -Characteristic 35 1 35 1.00 28.13 215.88 0.574 0.426 1.000 18.00 -1.0 72.1 3.3 1578 1556 275.5 7.3

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CALCULATION SHEET

Base Design Date: 14/03/12

General Details Base Design

Pmax = 352 295

Pmin = 197 129

Width of pressure ∆ 8.80 8.80

Rate of change of base reaction 18 19

Bearing pressure at stem/toe 309 250

Bearing pressure at stem/heel 295 235

Design moment for toe 900 684

Cover for base 40 40

Bar diametre 25 25

Effective depth, d 948 948

EN 1992-2 K 0.033 0.025

z 919 926

As 2252 1698

Design moment for toe 2860 2917

Cover for base 40 40

Bar diametre 25 25

Effective depth, d 948 948

EN 1992-2 K 0.106 0.108

z 848 846

As 7751 7924

The design is based on bearing pressure. And the reinforcement summary as follow: GEO Comb.1 GEO Comb.2

As required 7130 7329 As provided 8378 8378 Stem Reinforcement H40 @ 150 H40 @ 150 As required 2252 1698 As provided 3272 3272 Toe Reinforcement H25 @ 150 H25 @ 150 As required 7751 7924 As provided 8378 8378 Heel Reinforcement H40 @ 150 H40 @ 150 -Characteristic -Toe design Heel design -Characteristic