Sam Eurocode UK Pretressed Beam Sample Report

Sample Report Precast Pre-tensioned Beam Example Eurocodes UK NA

Pre-tensioned Pre-stressed Beam Bridge Design Example 1.

Geometry & Basic Data ................................................................................................................... 5

2.

Carriageway Configuration .................................................................................................. ...........9

3. 4.

Global Analysis Model................................................................................................................... 13 Influence surfaces ......................................................................................................................... 17 a) Mid Span Sagging Moment ....................................................................................................... 19 b) Internal Support Hogging Moment ........................................................................................... 20 c) Internal Support Shear .............................................................................................................. 21

5.

Traffic Loading Configuration........................................................................................................ 23 a) Mid Span Sagging Moment ....................................................................................................... 25 b) Internal Support Hogging Moment ........................................................................................... 26 c) Internal Support Shear .............................................................................................................. 27

6.

Global Analysis Results.................................................................................................................. 29 a) Mid Span Sagging Moment ....................................................................................................... 31 b) Internal Support Hogging Moment ........................................................................................... 33 c) Internal Support Shear .............................................................................................................. 35

7.

Section Properties ......................................................................................................................... 37 a) Mid Span ................................................................................................................................... 39 b) Internal Support ........................................................................................................................ 41

8.

Data Summary after Tendon Design ............................................................................................. 43

9.

Temperature Gradient .................................................................................................................. 51

10. Shrinkage & Creep ........................................................................................................................ 55 11. Verification: Transfer Stresses ...................................................................................................... 63 12. Verification: SLS Bending - Mid Span ............................................................................................ 73 13. Verification: ULS Bending - Mid Span ........................................................................................... 93 14. Verification: SLS bending – Pier .................................................................................................... 99 15. Verification: SLS bending – Support ............................................................................................ 117 16. Verification: ULS Shear - Pier ...................................................................................................... 135 17. Verification: ULS Interface Shear ................................................................................................ 143 18. Verification: Web Shear Cracking ............................................................................................... 149 Appendix - National Annex NDP Values.............................................................................................. 157

3

4

Pre-tensioned Pre-stressed Beam Bridge Design Example

1. Geometry & Basic Data

5

6

General Cross Section

Elevation

Plan

       

Grade C31/40 insitu concrete; Grade C50/60 precast concrete Grade B500B reinforcement steel Supports located 1m beneath soffit of slab Reinforced Concrete diaphragm over supports Cracked insitu concrete over central supports Slab reinforcement over internal supports (6m either side) Carriageway is 9.6 m wide with 1.2m footway on each side Designed for vertical highway loading groups Gr1a with French National Annex NDP values

7

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

 

USER NOTES

The design had been completed using the following process: 1) Four beams are created in SAM, two representing each span of the Y7 inner beams and the other two representing the edge beams of each span (with the upstand on the left hand side). At this stage all possible tendons are active. The differential temperatue profile is also determied and entered for each of the beams 2) A line beam analysis is carried out to determine the bending moments and shear forces atrributed to the dead load actions at each construction stage and the secondary moments and shears for differential temperatuire and differential shrinkage. Surfacing (SDL) actions are also established with the line beam analysis 3) A grillage model of the bridge deck is created using the beams prepared in 1) above. The grillage is to take account of the vertical level of each of the component beam elements by way of member eccentricities. This will give rise to a better distribution of effects but will intruduce (relatively small) axial forces into the beams. 4) Traffic load patterns are established for max sagging, hogging and shear for each node point along one of the central most beams, by using the load optimisation. This will give rise to three envelopes for sagging, hogging and shear. 5) The traffic live loads are transferred back to the table in the appropriate beam file. 6) An alaysis at transfer is carried out and some tendons are removed and debonded to reduce the compressive and tensile stresses to below limiting values. (This can be done with the tendon optimisation facility if required). Results output is produced for the mid span section 7) Other construction stages are checked at SLS Characteristic and ULS:STR to check compliance with stress limits and Bending capacity. Results output is produced for the mid span section. 8) Bending moments (sagging and Hogging) due to the full traffic action (plus other permanent and variable effects) ar checked for compliance at SLS and ULS. Results output is produced for the mid span section. 9) Transverse and Longitudinal shear reinforcement requirements are established and the results output for the most onerouse section as well as web shear cracking checks at SLS 10) Other reports of results, such as differential temp and shrinkage are produced and appended to the final report. 11) Time dependant creep effects are accounted for using the simplified method found in EN1992-2 Annex KK.7

SAM v6.50d

02/02/2012 10:57:11

© 2012 Bestech Systems Ltd

8

Page: 1

Pre-tensioned Pre-stressed Beam Bridge Design Example

2. Carriageway Configuration

9

10

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Job No.:   6.5d Calc. By:   DLG

Sample Reports

Structure: 2 span grillage prestresses beam deck Eurocodes + UK NA

Checked:   

Data File: J:\...\6.50d Data Files\2 span prestress beam deck .sst 02/02/2012 09:29:44

 

Data Report

STRUCTURE

CARRIAGEWAYS CW1: Carriageway Carriageway is for road traffic loading. It is aligned to design line DL1 and is single. Primary carriageway has 2 lanes 4.0m wide.  

Carriageway

Offset 1 (m)

Offset 2 (m)

Primary

-4.0

4.0

Footway 1

-5.5

-4.0

Footway 2

4.0

5.5

Loaded Widths for: CW1 CF1: Default Primary carriageway - Number of lanes: 2 Ref Offset Width Direction 1 0.0 3.0 with Chainage 2 3.0 3.0 against Chainage CF2: Load Opt. (created by load Primary carriageway - Number of Ref Offset Width 1 1.5 3.0 2 5.0 3.0

optimisation) lanes: 2 Direction with Chainage against Chainage

CF3: Load Opt. (created by load Primary carriageway - Number of Ref Offset Width 1 2.0 3.0 2 4.5 3.0

optimisation) lanes: 2 Direction with Chainage against Chainage

SAM v6.50d

02/02/2012 11:00:53

© 2012 Bestech Systems Ltd

11

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Job No.:   6.5d Calc. By:   DLG

Sample Reports

Structure: 2 span grillage prestresses beam deck Eurocodes + UK NA

Checked:   

Data File: J:\...\6.50d Data Files\2 span prestress beam deck .sst 02/02/2012 09:29:44

CF4: Load Opt. (created by load Primary carriageway - Number of Ref Offset Width 1 0.5 3.0 2 3.5 3.0

optimisation) lanes: 2 Direction with Chainage against Chainage

CF5: Load Opt. (created by load Primary carriageway - Number of Ref Offset Width 1 -0.25 2.5 2 3.5 3.0

optimisation) lanes: 2 Direction with Chainage against Chainage

CF6: Load Opt. (created by load Primary carriageway - Number of Ref Offset Width 1 0.0 3.0 2 5.0 3.0

optimisation) lanes: 2 Direction with Chainage against Chainage

CF7: Load Opt. (created by load Primary carriageway - Number of Ref Offset Width 1 0.0 3.0 2 4.5 3.0

optimisation) lanes: 2 Direction with Chainage against Chainage

CF8: Load Opt. (created by load Primary carriageway - Number of Ref Offset Width 1 0.0 3.0 2 3.5 3.0

optimisation) lanes: 2 Direction with Chainage against Chainage

SAM v6.50d

02/02/2012 11:00:53

© 2012 Bestech Systems Ltd

12

Page: 2

Pre-tensioned Pre-stressed Beam Bridge Design Example 3. Global Analysis Model

13

14

This is a view of the structure that is modelled for the global analysis highlighting the beam considered for design

The beam in isolation indicates the cracked concrete slab over the central pier, shown dotted

15

16

Pre-tensioned Pre-stressed Beam Bridge Design Example

4. Influence surfaces a) Mid Span Sagging Moment b) Internal Support Hogging Moment c) Internal Support Shear

17

18

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job: Sample Reports Structure: 2 span grillage prestresses beam deck Eurocodes + UK NA Data File: J:\Marketing\Sample Reports\Sam Eurocode UK Prestressed Beam\6.50d Data Files\2 span prestress beam deck .sst 02/02/2012 09:29:44 Result Type: Influence Surface

Job No.: 6.5d Calc. By: DLG Checked:

Name: I7: BM55; My Sagging

Influence coefficients are expressed with respect to global axes. Analysis Run: 01/02/2012 14:39:12 Results shown for: Influence Coefficients - DZ (m)

SAM v6.50d Copyright © 2012 Bestech Systems Ltd

02/02/2012 11:14

19

1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job: Sample Reports Structure: 2 span grillage prestresses beam deck Eurocodes + UK NA Data File: J:\Marketing\Sample Reports\Sam Eurocode UK Prestressed Beam\6.50d Data Files\2 span prestress beam deck .sst 02/02/2012 09:29:44 Result Type: Influence Surface

Job No.: 6.5d Calc. By: DLG Checked:

Name: I25: BM60; My Hogging

Influence coefficients are expressed with respect to global axes. Analysis Run: 06/02/2012 11:01:20 Results shown for: Influence Coefficients - DZ (m)

SAM v6.50d Copyright © 2012 Bestech Systems Ltd

06/02/2012 10:58

20

1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job: Sample Reports Structure: 2 span grillage prestresses beam deck Eurocodes + UK NA Data File: J:\Marketing\Sample Reports\Sam Eurocode UK Prestressed Beam\6.50d Data Files\2 span prestress beam deck .sst 02/02/2012 09:29:44 Result Type: Influence Surface

Job No.: 6.5d Calc. By: DLG Checked:

Name: I26: BM60; Shear z-

Influence coefficients are expressed with respect to global axes. Analysis Run: 06/02/2012 11:01:20 Results shown for: Influence Coefficients - DZ (m)

SAM v6.50d Copyright © 2012 Bestech Systems Ltd

06/02/2012 10:59

21

1

22

Pre-tensioned Pre-stressed Beam Bridge Design Example

5. Traffic Loading Configuration a) Mid Span Sagging Moment b) Internal Support Hogging Moment c) Internal Support Shear

23

24

25

26

27

28

Pre-tensioned Pre-stressed Beam Bridge Design Example

6. Global Analysis Results a) Mid Span Sagging Moment b) Internal Support Hogging Moment c) Internal Support Shear

29

30

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job No.: 6.5d Job: Sample Reports Calc. By: DLG Structure: 2 span grillage prestresses beam deck Checked: Eurocodes + UK NA Data File: J:\Marketing\Sample Reports\Sam Eurocode UK Prestressed Beam\6.50d D...\2 span prestress beam deck .sst 02/02/2012 09:29:44 Result Type: Envelope Result For: Beam

Name: E1: GR1A; ULS STR/GEO Mem 49-60: My+ Effect: Member End Actions

Moments at the member start end correspond with the local member axes directions. At the other end, moments are positive in the opposite direction to the local member axes. With this convention, a positive y or z moment at each end denotes sagging. The table displays the enveloped effect and associated values. The enveloped effect is Member End Moments - My (kN.m). Analysis Run: 01/02/2012 14:48:20 Results shown for: Member End Moments - My (kN.m)

New Selection Reference

Member End Forces Fx (kN)

Joint

49

53

-55.91424

47.25736

26.53076

25.44022

184.235

C1

182.2866

49

54

-35.84683

33.06124

271.1681

19.73986

335.773

C9

100.8609

50

54

-22.25784

22.6683

133.4978

23.78223

343.2836

C9

51.87468

50

55

54.62167

-2.692833

488.1098

-2.971709

1012.892

C17

-1.920841

51

55

20.41604

-2.863775

207.1184

1.268835

992.3741

C17

4.310352

51

56

28.14961

-3.108706

341.2957

0.4258882

1519.03

C25

7.980115

52

56

9.656585

-2.213639

12.84226

4.645401

1506.387

C25

8.499461

52

57

12.55014

-3.992453

271.0804

3.409645

1867.618

C33

11.38605

53

57

1.544886

-1.958322

-53.32979

7.16562

1859.024

C33

10.30689

53

58

2.67042

-3.684942

209.6595

5.880492

2039.232

C41

11.96043

54

58

0.7964923

-0.7758132

-115.5332

8.95645

2035.977

C41

11.81908

54

59

2.120291

-2.487774

138.1745

7.473753

2042.085

C49

10.77256

55

59

11.21513

0.7455683

-183.48

9.730765

2045.381

C49

12.77409

Load Ref

Fy (kN)

Member End Moments

Member

Fz (kN)

Mx (kN.m)

My (kN.m)

Unfactored

Type

Origin

Mz (kN.m)

Factors Gamma

Psi

Alpha

Factored gr

Lane

Other

Total

Compilation : C49: BM55; My Sagging; GR1A; ULS STR/GEO (SUM=2045.38) L57

LM1 UDL System

285.1668

1.35

1

0.61

1

1

1

234.8349

L59

LM1 UDL System

22.51277

1.35

1

2.2

1

1

1

66.86293

L121

Footway: UDL System (Footway)

9.465714

1.35

1

1

1

12.77871

L122

Footway: UDL System (Footway)

23.41097

1.35

1

1

1

31.60481

L123

LM1 UDL System

282.2928

1.35

1

2.2

1

0.2777778

1

232.8916

L124

LM1 Tandem System

649.1479

1.35

1

1

1

0.6666667

1

584.2331

L125

LM1 Tandem System

653.4628

1.35

1

1

1

1

1

1925.46

882.1748 My=2045.381

55

60

15.52078

0.798247

77.73588

7.514261

1895.5

C57

-17.79333

56

60

33.82052

-2.988016

-247.2278

2.884023

1907.151

C57

-16.04987

56

61

30.5347

0.8282612

-6.834788

5.464101

1621.272

C65

-15.22928

57

61

60.01271

-3.610685

-346.8961

0.3388024

1638.577

C65

-16.90568

57

62

48.37749

-4.715206

-110.8182

-0.6692659

1210.068

C73

-10.54859

58

62

82.86469

-10.92155

-465.8913

-5.560555

1230.844

C73

-17.32338

58

63

28.10417

-7.797547

-134.3832

-4.188907

651.3091

C81

-3.139501

59

63

52.21575

-12.04783

-505.8134

-5.459631

681.349

C81

-11.63125

59

64

5.630956

-9.655632

-151.3374

-7.84137

61.63301

C89

4.864394

60

64

11.72936

-13.57086

-406.9595

-8.120834

67.45666

C89

12.16619

60

65

-20.1954

-9.464386

-16.30567

-6.696705

7.586888

C97

20.18539

SAM v6.50d Copyright © 2012 Bestech Systems Ltd

02/02/2012 11:29

31

1

32

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job No.: 6.5d Job: Sample Reports Calc. By: DLG Structure: 2 span grillage prestresses beam deck Checked: Eurocodes + UK NA Data File: J:\Marketing\Sample Reports\Sam Eurocode UK Prestressed Beam\6.50d D...\2 span prestress beam deck .sst 02/02/2012 09:29:44 Result Type: Envelope Result For: Beam

Name: E2: GR1A; ULS STR/GEO Mem 49-60: MyEffect: Member End Actions

Moments at the member start end correspond with the local member axes directions. At the other end, moments are positive in the opposite direction to the local member axes. With this convention, a positive y or z moment at each end denotes sagging. The table displays the enveloped effect and associated values. The enveloped effect is Member End Moments - My (kN.m). Analysis Run: 01/02/2012 14:48:20 Results shown for: Member End Moments - My (kN.m)

New Selection Reference

Member End Forces Fx (kN)

Joint

49

53

157.8887

5.094982

427.0325

-2.139213

-540.7185

C2

49

54

137.6641

5.170721

207.8578

-4.97695

-203.0551

C10

-19.1692

50

54

99.32214

4.674887

210.546

-4.123625

-224.4301

C10

-1.098864

50

55

-2.612839

0.125463

-30.58831

-0.1607472

-70.21469

C26

-0.04289707

51

55

-0.8885847

0.4065817

-30.84254

-0.5053211

-69.16653

C26

0.2566332

51

56

-0.8885847

0.4065817

-30.84254

-0.5053211

-128.0478

C26

-0.5195683

52

56

1.513816

0.7835213

-31.26312

-0.8808424

-126.6603

C26

0.5482784

52

57

2.163933

1.11089

-33.71269

0.08934582

-189.3661

C42

-1.782311

53

57

7.540948

1.586132

-34.77629

-0.4991898

-186.3882

C42

0.3427496

53

58

7.498607

1.625769

-34.81647

-0.4645858

-252.8444

C58

-2.733323

54

58

14.86624

2.137992

-36.42122

-1.132049

-248.9295

C58

0.4624202

54

59

14.80931

2.121582

-36.50214

-1.130482

-318.4683

C74

-3.609668

55

59

24.70702

2.689951

-38.68139

-1.896179

-313.4238

C58

0.6104634

55

60

24.70534

2.664611

-38.80091

-1.896578

-387.4718

C74

-4.508079

56

60

37.70397

3.20602

-41.87492

-2.795453

-381.0251

C74

0.7231245

56

61

37.70397

3.20602

-41.87492

-2.795453

-460.9685

C74

-5.397487

57

61

54.36921

3.641991

-45.78775

-3.869674

-453.6171

C74

0.8188211

57

62

54.36921

3.641991

-45.78775

-3.869674

-541.0301

C74

-6.134068

58

62

74.1749

3.475636

-50.55485

-5.391563

-531.9109

C74

0.7229482

58

63

95.30983

2.989823

-90.50055

-4.804924

-656.2544

C82

-5.145004

59

63

117.8148

1.956679

-95.09197

-8.621091

-610.4323

C82

0.5380956

59

64

150.7005

-26.16291

-266.468

-23.02836

-888.0567

C90

24.02131

60

64

154.1473

-36.96983

-270.5991

-19.99131

-883.7671

C90

8.108403

60

65

190.1957

-15.75881

-469.0165

-9.477075

-1286.162

C98

13.65186

Load Ref

Fy (kN)

Member End Moments

Member

Fz (kN)

Mx (kN.m)

My (kN.m)

Unfactored

Type

Origin

Mz (kN.m) -0.3055404

Factors Gamma

Psi

Alpha

Factored gr

Lane

Other

Total

Compilation : C98: BM60; My Hogging; GR1A; ULS STR/GEO (SUM=-1286.16) L24

LM1 UDL System

-11.35887

1.35

1

1

-33.73584

L210

Footway: UDL System (Footway)

-0.2945362

1.35

1

1

1

-0.3976238

L211

Footway: UDL System (Footway)

-6.087952

1.35

1

1

1

-8.218735

L212

Footway: UDL System (Footway)

-4.697958

1.35

1

1

1

-6.342243

L213

Footway: UDL System (Footway)

-12.63796

1.35

1

1

1

-17.06124

L214

LM1 UDL System

-311.375

1.35

1

0.61

1

1

1

-256.4173

L215

LM1 Tandem System

-312.2353

1.35

1

1

1

1

1

-421.5176

L216

LM1 UDL System

-311.8849

1.35

1

2.2

1

0.2777778

1

-257.3051

L217

LM1 Tandem System

-298.1766

1.35

1

1

1

0.6666667

1

-268.3589

L218

LM1 UDL System

-5.659007

1.35

1

2.2

1

1

1

-1274.408

2.2

1

1

-16.80725 My=-1286.162



SAM v6.50d Copyright © 2012 Bestech Systems Ltd

02/02/2012 11:31

33

1

34

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job No.: 6.5d Job: Sample Reports Calc. By: DLG Structure: 2 span grillage prestresses beam deck Checked: Eurocodes + UK NA Data File: J:\Marketing\Sample Reports\Sam Eurocode UK Prestressed Beam\6.50d D...\2 span prestress beam deck .sst 02/02/2012 09:29:44 Result Type: Envelope Result For: Beam

Name: E9: GR1A; ULS STR/GEO Mem 50-60: Sh z Effect: Member End Actions

Forces at the member start end correspond with the local member axes directions. At the other end, forces are positive in the opposite direction to the local member axes. With this convention, a positive axial force at each end denotes compression. The table displays the enveloped effect and associated values. The enveloped effect is Member End Forces - Fz (kN). Analysis Run: 01/02/2012 14:48:20 Results shown for: Member End Forces - Fz (kN)

New Selection Reference

Member End Forces Fx (kN)

Joint

49

53

114.2916

-1.96579

525.8172

C105

-2.585628

-433.2182

-15.82357

49

54

114.2916

-1.96579

525.8172

C105

-2.585628

68.69836

-13.94714

50

54

60.94563

-1.625222

512.9767

C105

-1.151738

40.00968

-3.454434

50

55

60.94563

-1.625222

512.9767

C105

-1.151738

1019.329

-0.3517376

51

55

33.78914

-3.655797

426.0225

C113

2.064739

674.1985

-3.804586

51

56

33.78914

-3.655797

426.0225

C113

2.064739

1487.514

3.174661

52

56

14.18757

-4.877261

352.5722

C121

4.608999

1064.631

-4.992496

52

57

14.18757

-4.877261

352.5722

C121

4.608999

1737.724

4.318638

53

57

1.836164

-4.613297

289.4707

C129

5.606502

1238.806

-4.738815

53

58

1.836164

-4.613297

289.4707

C129

5.606502

1791.431

4.068386

54

58

-0.7389602

-3.216076

233.3123

C137

5.591374

1243.906

-3.223764

54

59

-0.7389602

-3.216076

233.3123

C137

5.591374

1689.32

2.91601

55

59

13.77622

-2.013512

-292.0244

C146

3.502448

1703.899

-10.56414

55

60

13.77622

-2.013512

-292.0244

C146

3.502448

1146.398

-6.720165

56

60

38.65846

5.128567

-363.1734

C154

6.038212

1668.201

11.65262

56

61

38.65846

5.128567

-363.1734

C154

6.038212

974.8671

1.861671

57

61

75.81142

5.968157

-428.0912

C162

4.055623

1443.039

11.47534

57

62

75.81142

5.968157

-428.0912

C162

4.055623

625.7743

0.08159752

58

62

110.6654

4.032943

-500.8601

C170

1.035365

1053.722

7.826455

58

63

110.6654

4.032943

-500.8601

C170

1.035365

97.5351

0.1272036

59

63

114.069

-0.4487549

-583.3914

C178

-1.563676

489.9939

1.894806

59

64

114.069

-0.4487549

-583.3914

C178

-1.563676

-623.7527

2.751519

60

64

86.18819

-2.104652

-655.6394

C186

-6.772206

-294.7813

4.316139

Load Ref

Fy (kN)

Member End Moments

Member

Fz (kN)

Origin

Mx (kN.m)

My (kN.m)

Unfactored

Mz (kN.m)

Factors

Type

Gamma

Psi

Alpha

Factored gr

Lane

Other

Total

Compilation : C186: BM60; Shear z-; GR1A; ULS STR/GEO (SUM=-655.64) L231

LM1 UDL System

-1.622997

1.35

1

2.2

1

1

1

-4.8203

L425

LM1 UDL System

-1.929261

1.35

1

2.2

1

1

1

-5.729905

L467

Footway: UDL System (Footway)

-0.7695409

1.35

1

1

1

-1.03888

L468

Footway: UDL System (Footway)

-2.989803

1.35

1

1

1

-4.036234

L469

Footway: UDL System (Footway)

-0.03466308

1.35

1

1

-0.04679515

L470

LM1 UDL System

-73.47056

1.35

1

2.2

1

0.2777778

1

-60.61321

L471

LM1 Tandem System

-143.3186

1.35

1

1

1

0.6666667

1

-128.9867

L472

LM1 UDL System

-118.1804

1.35

1

0.61

1

1

1

-97.32159

L473

LM1 Tandem System

-261.1537

1.35

1

1

1

1

1

-352.5574

L474

LM1 UDL System

-0.02488137

1.35

1

2.2

1

1

1

-0.07389768

L475

LM1 UDL System

-0.1395501

1.35

1

2.2

1

1

1

1

-603.6339

-0.4144637 Fz=-655.6394

60

65

86.18819

SAM v6.50d Copyright © 2012 Bestech Systems Ltd

-2.104652

-655.6394

C186

-6.772206

02/02/2012 11:35

35

-920.6156

6.325115

1

36

Pre-tensioned Pre-stressed Beam Bridge Design Example

7. Section Properties a) Mid Span b) Internal Support

37

38

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design code: Analysis:

EN 1992-2:2005 with UK National Annex (modified) Section Properties EN 1990 Equation 6.14 SLS Characteristic Exposure Class: XD1, XD2, XS1, XS2, XS3 Section Ref 1 at 10.5m from left end of beam

Section Ref: 1 "Section 1" depth of precast beam total depth of section

= 1300.0 mm = 1470.0 mm

Section properties are detailed below in the following sequence: PRECAST BEAM ALONE COMPOSITE BEAM TO STAGE 1

PRECAST BEAM ALONE Elastic section properties area, height to centroid, overall depth, 2nd moment of area, section modulus at bottom, section modulus at top,

Ac = 5.372E5 mm² za = 576.039 mm h = 1300.0 mm Iy y = 9.2977E10 mm⁴ Wb = 9.2977E10 / -576.04 -1.6141E8 mm³ Wt = 9.2977E10 / (1300.0-576.039) 1.28428E8 mm³

COMPOSITE BEAM COMPOSITE BEAM TO STAGE 1 Elastic section properties Area mm²

 

 

centroid mm

Sy mm³

Iy y mm⁴

Iy y (z=0) mm⁴

Precast beam

537225.68

Stage 1 i.s.

388869.57 1372.4329 1.057 5.04816E8 1.18215E9 6.9401E11

 

TOTAL

576.0392

α

1.0 3.09463E8 9.2977E10 2.7124E11

905051.14(transformed)

SAM v6.50d

8.14279E8

06/02/2012 10:28:43

© 2012 Bestech Systems Ltd

39

9.6525E11

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

height to centroid

= = Iy y = =

8.14279E8/9.051E5 899.705 mm 9.6525E11 - (9.051E5*899.705²) 2.3264E11 mm⁴

ELASTIC SECTION PROPERTIES SUMMARY TABLE Level mm

 

 

Iy y mm⁴

zn a mm

W mm³

Precast beam only Precast beam

B

0.0

T

1300.0

9.2977E10

576.0392

-1.6141E8 1.28428E8

In situ to stage 1 Precast beam In situ Stage 1

SAM v6.50d

B

0.0

T

1300.0

2.3264E11

899.70476

5.81164E8

B

1270.0

6.64191E8

T

1470.0

4.31262E8

06/02/2012 10:28:43

© 2012 Bestech Systems Ltd

40

-2.5857E8

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design code: Analysis:

EN 1992-2:2005 with UK National Annex (modified) Section Properties EN 1990 Equation 6.14 SLS Characteristic Exposure Class: XD1, XD2, XS1, XS2, XS3 Section Ref 2 at 21m from left end of beam

Section Ref: 2 "Section 2" depth of precast beam total depth of section

= 1300.0 mm = 1470.0 mm

Section properties are detailed below in the following sequence: PRECAST BEAM ALONE COMPOSITE BEAM TO STAGE 1

PRECAST BEAM ALONE Elastic section properties area, height to centroid, overall depth, 2nd moment of area, section modulus at bottom, section modulus at top,

Ac = 5.372E5 mm² za = 576.039 mm h = 1300.0 mm Iy y = 9.2977E10 mm⁴ Wb = 9.2977E10 / -576.04 -1.6141E8 mm³ Wt = 9.2977E10 / (1300.0-576.039) 1.28428E8 mm³

COMPOSITE BEAM COMPOSITE BEAM TO STAGE 1 Elastic section properties Area mm²

 

 

centroid mm

Sy mm³

Iy y mm⁴

Iy y (z=0) mm⁴

Precast beam

537225.68

Stage 1 i.s.

388869.57 1372.4329 1.057 5.04816E8 1.18215E9 6.9401E11

Rft in IS 1

4908.7385

 

TOTAL

576.0392

α

1407.5

1.0 3.09463E8 9.2977E10 2.7124E11 0.211

928282.4(transformed)

SAM v6.50d

3.2698E7 907471.06 8.46977E8

02/02/2012 11:41:05

© 2012 Bestech Systems Ltd

41

4.6E10 1.0113E12

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

height to centroid

= = Iy y = =

8.46977E8/9.283E5 912.413 mm 1.0113E12 - (9.283E5*912.413²) 2.3848E11 mm⁴

ELASTIC SECTION PROPERTIES SUMMARY TABLE Level mm

 

 

Iy y mm⁴

zn a mm

W mm³

Precast beam only Precast beam

B

0.0

T

1300.0

9.2977E10

576.0392

-1.6141E8 1.28428E8

In situ to stage 1 Precast beam In situ Stage 1

SAM v6.50d

B

0.0

T

1300.0

2.3848E11

912.41288

6.1529E8

B

1270.0

7.05066E8

T

1470.0

4.52167E8

02/02/2012 11:41:05

© 2012 Bestech Systems Ltd

42

-2.6137E8

Page: 2

Pre-tensioned Pre-stressed Beam Bridge Design Example

8. Data Summary after Tendon Design

43

44

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

 

DATA SUMMARY

ANALYSIS TYPE: EN 1992-2 Pre-tensioned Prestressed Beam With UK National Annex (modified) BEAM DETAILS Span:

Total length of pre-tensioned beam Distance from left support to beam end face Distance from right support to beam end face Total distance between supports

: : : :

21 m 0 m 0 m 21 m

Beam section varies along length of beam. Number of different sections No. of longitudinal construction stages No. of superimposed construction stages

: 2 : 2 : 1

Section 1

SAM v6.50d

02/02/2012 11:47:59

© 2012 Bestech Systems Ltd

45

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Precast beam: Precast beam is standard section: Y7 Beam Property set: 2 "C40/50 Ecm 35.2 " Age of beam at transfer: 4.0 days Corresponding concrete strength at transfer: 23.8094 MPa In situ concrete - stage 1A: In situ is from standard section: - width : 2.0 m - depth : 0.2 m Property set: 1 "C31/40 Ecm 33.3 " Age of beam when stage 1A concrete is cast: 60 days Shear resistance width:

216.0 mm

Section 2

Precast beam: Precast beam is standard section: Y7 Beam Property set: 2 "C40/50 Ecm 35.2 " Age of beam at transfer: 4.0 days Corresponding concrete strength at transfer: 23.8094 MPa In situ concrete - stage 1B: In situ is from standard section: - dimensions (m) : 2.0 0.0 0.2 0.0 0.0 0.0 Property set: 1 "C31/40 Ecm 33.3 " Age of beam when stage 1B concrete is cast: 60 days Shear resistance width:

SAM v6.50d

216.0 mm

02/02/2012 11:47:59

© 2012 Bestech Systems Ltd

46

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Tendons:  

 

y-z coordinates mm

area transmission coeffients mm² α1 α2 ηp 1 η1 ηp 2

φ mm

draw-in mm/beam

property ref

-275.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

-225.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

-175.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

-125.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

-75.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Debonded

0.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Debonded

75.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Debonded

125.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

175.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

225.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

275.0

60.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

-75.0

110.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Debonded

-25.0

110.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Debonded

25.0

110.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Debonded

75.0

110.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Debonded

-25.0

210.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

25.0

210.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

-25.0

260.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

25.0

260.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

-80.0

1200.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

80.0

1200.0

150.0

1.0 0.19

3.2

1.0

1.2 16.0

3.0

4 Full stress

Debonded Tendons:  

 

y-z coordinates mm

distance from left end (m) start end

-75.0

60.0

2.0

19.0

0.0

60.0

2.0

19.0

75.0

60.0

2.0

19.0

-75.0

110.0

2.5

18.5

-25.0

110.0

2.5

18.5

25.0

110.0

2.5

18.5

75.0

110.0

2.5

18.5

SAM v6.50d

02/02/2012 11:47:59

© 2012 Bestech Systems Ltd

47

Page: 3

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Reinforcement:  

 

y-z coordinates mm

diameter mm

Property ref

Start m

End m

Length m

900.0

1407.5

25.0

3

15.0

21.0

6.0

700.0

1407.5

25.0

3

15.0

21.0

6.0

500.0

1407.5

25.0

3

15.0

21.0

6.0

300.0

1407.5

25.0

3

15.0

21.0

6.0

100.0

1407.5

25.0

3

15.0

21.0

6.0

-100.0

1407.5

25.0

3

15.0

21.0

6.0

-300.0

1407.5

25.0

3

15.0

21.0

6.0

-500.0

1407.5

25.0

3

15.0

21.0

6.0

-700.0

1407.5

25.0

3

15.0

21.0

6.0

-900.0

1407.5

25.0

3

15.0

21.0

6.0

Location of sections  

 

 

Position along span from left support: dimension (m) proportion

Section

0.0

0.0

1

"Section 1"

18.0

0.857

1

"Section 1"

18.0

0.857

2

"Section 2"

21.0

1.0

2

"Section 2"

PROPERTIES DETAILS ref: 1

Type: Concrete - Parabola-Rectangle Name: C31/40 Ecm 33.3

Design Code Part Characteristic strength

: fc k : fc k , c u b e : modulus of elasticity Ec m : Elastic modulus - long term : Ultimate compressive strain εc u : Tensile strength fc t m : Cement Class : Contains Silica Fume : Coefficient of thermal expansion: Density : Density increase for rft. :

SAM v6.50d

EN 1992-2 31.875 MPa 40.0 MPa 33.314469 GPa 13.325787 GPa 0.0035 -3.015931 MPa N - Normal and rapid hardening No 0.00001 /°C 24.0 kN/m³ 1.0 kN/m³

02/02/2012 11:47:59

© 2012 Bestech Systems Ltd

48

Page: 4

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

ref: 2

Type: Concrete - Parabola-Rectangle Name: C40/50 Ecm 35.2

Design Code Part Characteristic strength

: fc k : fc k , c u b e : modulus of elasticity Ec m : Elastic modulus - long term : Ultimate compressive strain εc u : Tensile strength fc t m : Cement Class : Contains Silica Fume : Coefficient of thermal expansion: Density : Density increase for rft. :

ref: 3

Type: Reinforcing Steel - Horizontal Name: Grade 500 Es 200.0

Yield strength modulus of elasticity Characteristic strain limit Density

ref: 4

EN 1992-2 40.0 MPa 50.0 MPa 35.220462 GPa 14.088185 GPa 0.0035 -3.508821 MPa N - Normal and rapid hardening No 0.00001 /°C 24.0 kN/m³ 1.0 kN/m³

fy k : Es : εu k : :

500.0 MPa 200.0 GPa 0.025 77.0 kN/m³

Type: Prestressing Steel - Horizontal Name: Grade 1600 Ep 195.0

tensile strength fp k : 0,1% proof stress fp 0 , 1 k : modulus of elasticity Ep : Relaxation loss after 1000 hours: Relaxation Class : Density :

1860.0 1600.0 195.0 8.0 1 77.0

MPa MPa GPa % kN/m³

ANALYSIS DATA Data for loss calculations:

%

Shrinkage strain is calculated from the data provided Creep coefficient is calculated from the data provided Differential shrinkage is calculated from the data provided Percentage of total long term loss which occurs before the section is made composite is 30.18 Age at start of drying shrinkage Ambient relative humidity Ambient temperature Maximum Curing temperature

= = = =

1.0 80.0 20.0 20.0

day % °C °C

Creep calculations are based upon EN 1992-1-1

SAM v6.50d

02/02/2012 11:47:59

© 2012 Bestech Systems Ltd

49

Page: 5

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Data for shear calculations: Material property for transverse reinforcement: Grade 500 Es 200.0 Angle between concrete strut and beam axis, θ = 35.0° Angle between shear reinforcement and beam axis, α = 90.0° Enhancement close to supports is ignored Surface condition for precast / in-situ interface = Smooth Longitudinal force ratio β is calculated Angle for compression strut in slab, θf = 26.0°

SAM v6.50d

02/02/2012 11:47:59

© 2012 Bestech Systems Ltd

50

Page: 6

Pre-tensioned Pre-stressed Beam Bridge Design Example

9. Temperature Gradient

51

52

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

DIFFERENTIAL TEMPERATURE EN 1991-1-5:2003 Figure 6.2 non-linear Temperature Profile

EN 1991-1-5:2003 Figure 6.2 non-linear Temperature Profile Figure 6.2c: Type 3b. Concrete Beams Surfacing : surfaced Surfacing thickness : 0.1 m  

 

Top warmer than bottom height m Temperature °C

Bottom warmer than top height m Temperature °C

0.0

13.5

0.0

-8.376

0.15

3.0

0.25

-0.56

0.4

0.0

0.45

0.0

1.27

0.0

1.02

0.0

1.47

2.5

1.22

-1.03

1.47

-6.488

Relaxing Forces Moment kN.m

Axial kN

Heating Temperature difference

-413.8371

-1015.993

Cooling Temperature difference

143.38408

976.55933

 

 

Note: The reinforcement has been ignored in the calculation of the above relaxing moments

Self Equilibrating Stresses

SAM v6.50d

02/02/2012 11:50:10

© 2012 Bestech Systems Ltd

53

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Rectangle  

 

Distance to top of section - m

Stress Heating

0.0

2.4760279

0.15

-0.769597

0.2

-0.885352

- MPa Cooling -1.437326 0.5291631

Y7 Beam  

 

Distance to top of section - m

Stress Heating

0.17

-0.862578

0.25 0.4

0.2475882 1.0791869

-1.425518

0.45

1.1531531

1.02

0.8018382

1.22

SAM v6.50d

- MPa Cooling

0.3157990

1.27

0.1221205

1.47

1.358411

-1.760619

02/02/2012 11:50:10

© 2012 Bestech Systems Ltd

54

Page: 2

Pre-tensioned Pre-stressed Beam Bridge Design Example 10.

55

Shrinkage & Creep

56

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

 

DIFFERENTIAL SHRINKAGE MODIFIED BY CREEP - Primary Load effects

Section Reference: 2

"Section 2"

Evaluate the shrinkage strains using EN 1992-1-1 clause 3.1.4(6) Shrinkage in precast at time t = ∞ Age of concrete at time considered, t = ∞ Age of concrete at loading, t0 = 4.0 days Age of concrete at start of drying, ts = 1.0 days Relative humidity of enviroment, RH = 80.0 % Average temperature, Ta = 20.0 °C Type of cement = Class N for which, EN1992-1-1 Annex B.1(2) α = 0.0 Annex B.2(1) αd s 1 = 4.0 Annex B.2(1) αd s 2 = 0.12 3.1.2(6) s = 0.25 Characteristic strength of concrete, fc k = 40.0 MPa Mean compressive strength at 28 days (Table 3.1), fc m = fc k + 8.0 = 48.0 MPa Mean comp. strength at 4.0 days (3.1.2(6) ), fc m (t0 ) = fc m .exp[s.(1-√(28/t0 )] = 48.0*exp[0.25*(1-√(28/4.0)] = 31.809 MPa Constant value from Annex B.2(1) fc m 0 = 10.0 MPa Total Shrinkage: εc s = εc d + εc a

SAM v6.50d

(3.8)

02/02/2012 11:54:19

© 2012 Bestech Systems Ltd

57

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Drying Shrinkage - Expression (3.9): εc d (t) = βd s (t,ts ).kh .εc d , 0 βd s (t,ts ) = 1.0 for t = ∞ From Table 3.3: kh = 0.79438 From Annex B, Expression (B.11):

-6

εc d , 0 = 0.85[(220+110.αd s 1 ).(exp(-αd s 2 .fc m /fc m 0 )].10 .βR H βR H = 1.55[1.0-(RH/100)³] (B.12) = 0.7564 For cement class N, αd s 1 = 4 αd s 2 = 0.12 hence, -6

εc d , 0 = 0.85[(220+110*4.0)*exp(-0.12*48.0/10.0)]*10 *0.7564 -6

and,

= 238.54*10

εc d (t) = 1.0*0.79438*238.54*10

-6

-6

= 189.491*10

Autogenous Shrinkage - Expression (3.11): εc a (t) = βa s (t).εc a (∞) βa s (t) = 1.0 for t = ∞ εc a (∞) = 2.5*(fc k -10.0)*10 -6 = 75.0*10 hence, εc a (t) = 1.0*75.0*10 = 75.0*10

-6

-6

-6

Total Shrinkage: εc s = εc d (t) + εc a (t) = 189.49131 + 75.0 = 264.49131*10

-6

Shrinkage in in-situ concrete at time t = ∞ Age of concrete at time considered, Age of concrete at loading, Age of concrete at start of drying, Relative humidity of enviroment, Average temperature, Type of cement for which, EN1992-1-1 Annex B.1(2) Annex B.2(1) Annex B.2(1) 3.1.2(6)

SAM v6.50d

t t0 ts RH Ta

α αd s 1 αd s 2 s

= ∞ = 4.0 days = 1.0 days = 80.0 % = 20.0 °C = Class N = 0.0 = 4.0 = 0.12 = 0.25

02/02/2012 11:54:19

© 2012 Bestech Systems Ltd

58

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Characteristic strength of concrete, fc k = 31.875 MPa Mean compressive strength at 28 days (Table 3.1), fc m = fc k + 8.0 = 39.875 MPa Mean comp. strength at 4.0 days (3.1.2(6) ), fc m (t0 ) = fc m .exp[s.(1-√(28/t0 )] = 39.875*exp[0.25*(1-√(28/4.0)] = 26.425 MPa Constant value from Annex B.2(1) fc m 0 = 10.0 MPa Total Shrinkage: εc s = εc d + εc a

(3.8)

Drying Shrinkage - Expression (3.9): εc d (t) = βd s (t,ts ).kh .εc d , 0 βd s (t,ts ) = 1.0 for t = ∞ From Table 3.3: kh = 0.79438 From Annex B, Expression (B.11):

-6

εc d , 0 = 0.85[(220+110.αd s 1 ).(exp(-αd s 2 .fc m /fc m 0 )].10 .βR H βR H = 1.55[1.0-(RH/100)³] (B.12) = 0.7564 For cement class N, αd s 1 = 4 αd s 2 = 0.12 hence, -6

εc d , 0 = 0.85[(220+110*4.0)*exp(-0.12*39.88/10.0)]*10 *0.7564 -6

and,

= 262.969*10

εc d (t) = 1.0*0.79438*262.969*10

-6

-6

= 208.897*10

Autogenous Shrinkage - Expression (3.11): εc a (t) = βa s (t).εc a (∞) βa s (t) = 1.0 for t = ∞ εc a (∞) = 2.5*(fc k -10.0)*10 -6 = 54.6875*10 hence, εc a (t) = 1.0*54.6875*10

-6

-6

-6

= 54.6875*10

Total Shrinkage: εc s = εc d (t) + εc a (t) = 208.89738 + 54.6875 = 263.58488*10

-6

Shrinkage in precast at time in-situ is placed (t = 60 days)

SAM v6.50d

02/02/2012 11:54:19

© 2012 Bestech Systems Ltd

59

Page: 3

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Age of concrete at time considered, t = 60.0 days Age of concrete at loading, t0 = 4.0 days Age of concrete at start of drying, ts = 1.0 days Relative humidity of enviroment, RH = 80.0 % Average temperature, Ta = 20.0 °C Type of cement = Class N for which, EN1992-1-1 Annex B.1(2) α = 0.0 Annex B.2(1) αd s 1 = 4.0 Annex B.2(1) αd s 2 = 0.12 3.1.2(6) s = 0.25 Characteristic strength of concrete, fc k = 40.0 MPa Mean compressive strength at 28 days (Table 3.1), fc m = fc k + 8.0 = 48.0 MPa Mean comp. strength at 4.0 days (3.1.2(6) ), fc m (t0 ) = fc m .exp[s.(1-√(28/t0 )] = 48.0*exp[0.25*(1-√(28/4.0)] = 31.809 MPa Constant value from Annex B.2(1) fc m 0 = 10.0 MPa Total Shrinkage: εc s = εc d + εc a

(3.8)

Drying Shrinkage - Expression (3.9): εc d (t) = βd s (t,ts ).kh .εc d , 0 βd s (t,ts ) = (t-ts )/[(t-ts )+0.04√h0 ³]

(3.10)

t-ts = 60.0-1.0 = 59.0 days βd s (t,ts ) = 59.0/(59.0+0.04√255.62³) = 0.26519 From Table 3.3: kh = 0.79438 From Annex B, Expression (B.11):

-6

εc d , 0 = 0.85[(220+110.αd s 1 ).(exp(-αd s 2 .fc m /fc m 0 )].10 .βR H βR H = 1.55[1.0-(RH/100)³] (B.12) = 0.7564 For cement class N, αd s 1 = 4 αd s 2 = 0.12 hence, -6

εc d , 0 = 0.85[(220+110*4.0)*exp(-0.12*48.0/10.0)]*10 *0.7564 -6

and,

= 238.54*10

εc d (t) = 0.26519*0.79438*238.54*10

-6

-6

= 50.2528*10

SAM v6.50d

02/02/2012 11:54:19

© 2012 Bestech Systems Ltd

60

Page: 4

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Autogenous Shrinkage - Expression (3.11): εc a (t) = βa s (t).εc a (∞) βa s (t) = 1-exp(-0.2√t) = 1.0-exp(-0.2*√60.0) = 0.78758 εc a (∞) = 2.5*(fc k -10.0)*10 -6 = 75.0*10 hence,

(3.13)

-6

-6

εc a (t) = 0.78758*75.0*10 -6

= 59.0686*10

Total Shrinkage: εc s = εc d (t) + εc a (t) = 50.252794 + 59.068556 = 109.32135*10

-6

Summary of data Section is composite from t = 60 days at time t = 60 days:

shrinkage strain in precast concrete, at time t = ∞

εa = 109.321 x10

shrinkage strain in in-situ concrete, differential shrinkage strain, εd i f f = εc - ( εb - εa )

εc = 263.585 x10

shrinkage strain in precast concrete,

εb = 264.491 x10

= 263.585 - (264.491-109.321) = 108.415 x10 creep coefficient, φ = 2.00881

-6

-6 -6

-6

(-φ)

1 - e creep reduction factor Φ = ——————————— φ 2nd moment of area of transformed section, Iy y height of centroid, za total transformed area, Ac elastic modulus of precast concrete, Ec , p elastic modulus of in situ concrete, Ec , i modular ratio

SAM v6.50d

= 0.43102 = = = = =

2.33E11 899.705 9.051E5 35.2205 33.3145

mm⁴ mm mm² GPa GPa

n0 = Ec , p / Ec , i = 35.2205/33.3145 = 1.05721

02/02/2012 11:54:19

© 2012 Bestech Systems Ltd

61

Page: 5

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Stage 1 In-situ area of concrete : 3.889E5 mm² height to centroid : 1372.43 mm force required to restrain shrinkage: Ac .Φ.Ec , i .εd i f f = = corresponding moment = =

-6

3.889E5*0.65982*33.3145*108.415 x10 605.383 kN 605.383*(1372.43-899.705) 286.182 kN.m (sagging)

self equilibrating stress in precast beam: top of beam = P/Ac + M/Wt = 605.38331/905051.14 + 286.18174/5.81164E8 = 1.1613224 MPa soffit of beam

= P/Ac + M/Wb = 605.38331/905051.14 + 286.18174/-2.5857E8 = -0.437889 MPa

self equilibrating stress in stage 1 concrete: at top = ( P/Ac + M.(zt -za )/Iy y + Φ.εd i f f .Ec , p )/α = (605.38331/905051.14 + 286.18174*570.29524/2.3264E11 + 0.4310270*-1.084E-4*35.220462 ) /1.0572122 = -0.260490 MPa at bottom

SAM v6.50d

= ( P/Ac + M.(zb -za )/Iy y + Φ.εd i f f .Ec , c )/α = (605.38331/905051.14 + 286.18174*370.29524/2.3264E11 + 0.4310270*-1.084E-4*35.220462) /1.0572122 = -0.493208 MPa

02/02/2012 11:54:19

© 2012 Bestech Systems Ltd

62

Page: 6

Pre-tensioned Pre-stressed Beam Bridge Design Example

11.

Verification: Transfer Stresses

63

64

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design code: EN 1992-2:2005 with UK National Annex (modified) Analysis: Stresses at Transfer EN 1990 Equation 6.14 SLS Characteristic Section Ref 1 at 10.5m from left end of beam

Section details:

Ref 1 "Section 1" at 0.5 x span = 10.5 m from left end of beam

Analysis:

Stresses at Transfer Serviceability Limit State: Characteristic

- EN 1990 Equation 6.14

ACTUAL STRESSES IN PRECAST BEAM No. of tendons fully bonded at this section: No. of tendons fully debonded at this section: No. of tendons deflected at this section:

SAM v6.50d

21 0 0

15/02/2012 15:36:54

© 2012 Bestech Systems Ltd

65

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Maximum Stressing Force - EN 1992-1-1 Clause 5.10.2.1(1)P For tendon property Grade 1600 Ep 195.0 k1 .fp k = 0.8*1860.0 = 1488.0 MPa k2 .fp 0 , 1 k = 0.9*1600.0 = 1440.0 MPa Wedge draw-in loss Clause 5.10.4(1)(i) draw-in strain = 0.003/21.0 = 1.43E-4 loss = Ep . strain = 195.0*1.43E-4 = 27.8571 MPa Heat Curing Clause 5.10.4(1)(ii)(Note) Concrete is cured at ambient temperature

Immediate Losses - EN 1992-1-1 Clause 5.10.4  

 

height No of mm tendons 60.0

 

fp MPa

k1 /k2

draw-in MPa

heat cure MPa

area mm²

initial force kN

11

1600.0

0.9

27.8571

0.0

150.0

2330.0357

110.0

4

1600.0

0.9

27.8571

0.0

150.0

847.28571

210.0

2

1600.0

0.9

27.8571

0.0

150.0

423.64286

260.0

2

1600.0

0.9

27.8571

0.0

150.0

423.64286

1200.0

2

1600.0

0.9

27.8571

0.0

150.0

423.64286

TOTAL

21

4448.25

In accordance with clause 5.10.9(1), for SLS, the Characteristic value must be used. With ri n f = 1.0, Pk , i n f = 4448.25 kN

Friction Clause 5.10.4(1)(i)

All tendons are straight in this beam.

Initial Relaxation Clause 5.10.4(1)(ii)

Loss is calculated from clause 3.3.2(7) For tendon property Grade 1600 Ep 195.0 relaxation loss at 1000 hours, ρ1 0 0 0 = 8.0 % μ = σp i / fp k = 1440.0-27.8571-0.0/1860.0 = 0.75921 time after tensioning = 96.0 hours for Class 1 relaxation, use Expression (3.28) 6.7μ

0.75(1-μ)

5.39 . ρ1 0 0 0 . e . [t/1000] . 10 -5 = 5.39 * 8.0 * 161.863 * 0.65495 * 10 = 0.04571

SAM v6.50d

-5

15/02/2012 15:36:54

© 2012 Bestech Systems Ltd

66

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

relaxation

 

 

 

height No of mm tendons 60.0

 

area x σp i

%

After relaxation loss kN

force kN

moment kN.m

11

2330.04 4.57 106.51239

2223.5233

133.4114

110.0

4

847.286 4.57 38.731779

808.55394

88.940933

210.0

2

423.643 4.57 19.365889

404.27697

84.898163

260.0

2

423.643 4.57 19.365889

404.27697

105.11201

1200.0

2

423.643 4.57 19.365889

404.27697

485.13236

4244.9082

897.49487

TOTAL

21

Moment about the centroid of the precast beam: Mr = 897.49487-(4244.9082*0.5760392) = -1547.739 kN.m Corresponding stresses: top stress = 4244.9082/537225.68+-1547.739/1.2843E8 = 7.9015362+-12.05139 = -4.149853 MPa bottom stress = 4244.9082/537225.68+-1547.739/-1.614E8 = 7.9015362+9.5890175 = 17.490554 MPa Self weight moment: c.s.a. = 5.372E5 mm²

[1]

density = 24.0 kN/m³ + 1.0 kN/m³ + 1.0 kN/m³ = 26.0 kN/m³ self weight = 5.372E5*26.0 = 13.9679 kN/m beam length = 21.0 m distance = 10.5 m Ms w = 0.5*13.9679*10.5*(21.0-10.5) = 769.979 kN.m Corresponding stresses: top stress = 769.979/1.2843E8 = 5.9954 MPa bottom stress = 769.979/-1.614E8 = -4.7704 MPa

Elastic Deformation - Clause 5.10.4(1)(iii) stress at top of precast beam stress at bottom of precast beam depth of precast beam elastic modulus of concrete at transfer

SAM v6.50d

= 1.84555 MPa = 12.7201 MPa = 1300.0 mm = 31.1307 GPa

15/02/2012 15:36:54

© 2012 Bestech Systems Ltd

67

Page: 3

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

 

height

 

 

mm 60.0

 

No of tendons

conc stress MPa

conc strain

tendon force kN

tendon moment kN.m

11

12.21824

3.925E-4

126.28096

7.5768575

110.0

4

11.79999

3.79E-4

44.348407

4.8783248

210.0

2

10.96348

3.522E-4

20.602262

4.326475

260.0

2

10.54523

3.387E-4

19.816291

5.1522358

1200.0

2

2.682055

8.615E-5

5.0400412

6.0480495

216.08796

27.981943

TOTAL

21

Moment about the centroid of the precast beam: Me d = 27.981943-(216.08796*0.5760392) = -96.49319 kN.m hence, top stress = 1.8455-216.08796/537.22568--96.49319/1.2843E8 = 1.8455-0.4022294--0.751339 = 2.1946575 MPa bottom stress = 12.72-216.08796/537.22568--96.49319/-1.614E8 = 12.72-0.4022294-0.5978237 = 11.720096 MPa After a further 2 iterations of the above process, the top and bottom stresses are as follows: top stress = 2.16502461 MPa bottom stress = 11.7912468 MPa

Max Prestress Force after transfer - EN 1992-1-1 Clause 5.10.3.(2) For tendon property Grade 1600 Ep 195.0 k7 .fp k = 0.75*1860.0 = 1395.0 MPa k8 .fp 0 , 1 k = 0.85*1600.0 = 1360.0 MPa Maximum tendon stress after transfer = 1329.4 MPa which is not greater than 1360.0 and therefore OK.

TOTAL LOSS OF PRESTRESS SUMMARY Initial stressing force Prestress after all transfer losses

= 4448.25 kN = 4043.05 kN

Corresponding loss = 9.11 %

LIMITING STRESSES IN PRECAST BEAM Compression EN 1992-1-1 Clause 3.1.2(5) & 3.1.2(6) For transfer at t = 4.0 days fc k (t) = fc m (t) = βc c (t) = for Class N cement,

SAM v6.50d

fc m (t) - 8.0 βc c (t).fc m exp{s[1-√(28/t)]} s = 0.25

Equation 3.1 Equation 3.2

15/02/2012 15:36:54

© 2012 Bestech Systems Ltd

68

Page: 4

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

hence

βc c (t) = = fc m = = fc m (t) = = and fc k (t) = =

exp{0.25[1.0-√28/4.0)]} 0.66269 fc k + 8.0 (from Table 3.1) 48.0 MPa 0.66269*48.0 31.8094 31.8094 - 8.0 MPa 23.8094 MPa

EN 1992-1-1 Clause 5.10.2.2(5) σc

35.0 MPa 1-RH/100 φR H = [ 1 + ——————————— . α1 ] .α2 0.33 0.1*h0 α1 = [35.0/48.0] α2 = [35.0/48.0] α3 = [35.0/48.0]

0.7 0.2 0.5

Expression (B.3b)

= 0.80163 = 0.93878 = 0.85391

φR H = [1.0 + (1.0-0.8) / (0.1*249.811 = 1.17777

0.33

) * 0.80163]*0.93878

β(fc m ) = 16.8/√fc m = 16.8/√48.0 = 2.42487

For Permanent Loads

In the absence of heat curing t0 , T =

SAM v6.50d

Expression (B.4)

4.0 days

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

80

Page: 6

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

age is adjusted for expression (B.5) (for cement type and temperature) - for cement class N (α = 0) 9.0

t0 = t0 , T . [ —————————————— + 1.0 ]

= 4.0 =

2.0 + t0 , T 9.0

α

* [ —————————————— + 1.0 ]

2.0 + 4.0 4.0 day

>=0.5

1.2

Expression (B.9)

0

1.2

0.2

β(t0 ) = 1/(0.1+t0 ) 0.2 = 1/(0.1+4.0 ) = 0.70446 βc (t,t0 ) = 1.0 for time t = ∞ hence from (B.1) and (B.2): φ(t,t0 ) = 1.17777*2.42487*0.70446 = 2.01193

Expression (B.5)

Check for creep non-linearity EN 1992-1-1 clause 3.1.4(4) At the level of the centroid of the tendons, the compressive stress in the concrete at time t0 = 8.31165 MPa. This does not exceed 0.45*fck(t0), i.e. 18.0 MPa, so non-linear creep is not considered

Shrinkage Strain for concrete - EN 1992-1-1 clause 3.1.4(6) Total Shrinkage: εc s = εc d + εc a

(3.8)

Drying Shrinkage - Expression (3.9): εc d (t) = βd s (t,ts ).kh .εc d , 0 βd s (t,ts ) = 1.0 for t = ∞ From Table 3.3: kh = 0.80018 From Annex B, Expression (B.11):

-6

εc d , 0 = 0.85[(220+110.αd s 1 ).(exp(-αd s 2 .fc m /fc m 0 )].10 .βR H βR H = 1.55[1.0-(RH/100)³] (B.12) = 0.7564 For cement class N, αd s 1 = 4 αd s 2 = 0.12 hence, -6

εc d , 0 = 0.85[(220+110*4.0)*exp(-0.12*48.0/10.0)]*10 *0.7564 -6

= 238.54*10

SAM v6.50d

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

81

Page: 7

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

and,

εc d (t) = 1.0*0.80018*238.54*10

-6

-6

= 190.877*10

Autogenous Shrinkage - Expression (3.11): εc a (t) = βa s (t).εc a (∞) βa s (t) = 1.0 for t = ∞ εc a (∞) = 2.5*(fc k -10.0)*10 -6 = 75.0*10 hence, εc a (t) = 1.0*75.0*10 = 75.0*10

-6

-6

-6

Total Shrinkage: εc s = εc d (t) + εc a (t) = 190.87688 + 75.0 = 265.87688*10

-6

Further Relaxation Clause 5.10.6(1)(b) Loss is calculated from clause 3.3.2(7) For tendon property Grade 1600 Ep 195.0 relaxation loss at 1000 hours, ρ1 0 0 0 = 8.0 % time after tensioning = 500000.0 hours μ = 0.75921 (as calculated for initial relaxation loss above) for Class 1 relaxation, use Expression (3.28) 6.7μ

0.75(1-μ)

-5

5.39 . ρ1 0 0 0 . e . [t/1000] . 10 -5 = 5.39 * 8.0 * 161.863 * 3.07185 * 10 = 0.21440 With the initial relaxation deducted, the variation in tendon stress from relaxation becomes: Δσp r / σp i = 0.21440 - 0.04571 = 0.16868 Summary of the above for Expression (5.46):

Estimated shrinkage strain εc s Creep coefficient at t for loading at t0 φ(t,t0 ) Relaxation, Δσp r Modulus of elasticity for prestressing steel Ep Modulus of Elasticity for concrete Ec m Area of all prestressing Ap Area of concrete section Ac Second moment of area of concrete section Ic

SAM v6.50d

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

82

= = = = = = = =

265.877 2.01193 238.212 195.0 37.9636 3150.0 9.051E5 2.33E11

-6

x10 MPa GPa GPa mm² mm² mm⁴

Page: 8

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Ep /Ec m Ep /Ec m .Ap /Ac Ac /Ic

= 195.0/37.9636 = 5.1365*3150.0/9.051E5 = 9.051E5/2.33E11

= 5.1365 = 0.01788 = 3.8904

In the table below the following vary with tendon height: σc , Q P = Stress in concrete adjacent to tendons zc p = Section centre of gravity to tendons φ(t,t0 ) = Creep Coefficient (if non-linear creep is considered)  

 

height

 

 

mm

Ap mm²

shrink εc s .Ep MPa

relax 0.8Δσp r MPa

φ(t,t0 )

51.846 190.57 2.012

σc , Q P MPa

creep Ep /Ec m .φ.σ MPa

denom ΔPc + s + r kN

zc p mm

60.0

1650.0

110.0

600.0

51.846 190.57 2.012 8.5109 87.954 789.705

8.605 88.927 839.705 1.175 465.43833

210.0

300.0

51.846 190.57 2.012 8.3226 86.008 689.705 1.133 86.962166

260.0

300.0

51.846 190.57 2.012 8.2284 85.035 639.705 1.121 87.637686

1200.0

300.0

51.846 190.57 2.012 6.4583 66.742

1.16 170.90467

-300.3 1.063 87.248992

Total force loss: Total moment loss:

 

 

898.19184 192.47246

Mc s r = 192.47246-(898.19184*0.8997047) = -615.635 kN.m

Corresponding stresses - before composite: top stress = ( 898.192/5.372E5+-615.64/1.284E8 )* 0.286 = ( 1.6719079+-4.793611 )* 0.286 = -0.893716 MPa bottom stress = ( 898.192/5.372E5+-615.64/-1.61E8 )* 0.2862 = ( 1.6719079+3.8141679 )* 0.286 = 1.5706162 MPa top stress bottom stress

= = = = = =

- after composite: ( 898.192/9.051E5+-615.64/5.812E8 )*(1.0- 0.286) ( 0.9924210+-1.059313 )*(1.0-0.286) -0.047742 MPa ( 898.192/9.051E5+-615.64/-2.59E8 )*(1.0-0.286 ) ( 0.9924210+2.3809161 )*(1.0-0.286) 2.4075798 MPa

Surfacing 1 Loading

MA p p l i e d = 99.65918 kN.m Corresponding stresses: top stress = 99.65918/5.8116E8 = 0.17148 MPa bottom stress = 99.65918/-2.586E8 = -0.3854 MPa

SAM v6.50d

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

83

Page: 9

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Traffic gr1a TS - for Bending design 1 Loading

MA p p l i e d = 934.3025 kN.m PA p p l i e d = -43.8224 kN Corresponding stresses: top stress = -43.8224/905051.1 + 934.3025/5.8116E8 = -0.0484 + 1.60764 = 1.55922 MPa bottom stress = -43.8224/905051.1 + 934.3025/-2.586E8 = -0.0484 + -3.613 = -3.6618 MPa

Traffic gr1a UDL - for Bending design 1 Loading

MA p p l i e d = 324.4073 kN.m PA p p l i e d = -4.365749 kN Corresponding stresses: top stress = -4.365749/905051.1 + 324.4073/5.8116E8 = -0.0048 + 0.55820 = 0.55337 MPa bottom stress = -4.365749/905051.1 + 324.4073/-2.586E8 = -0.0048 + -1.255 = -1.2594 MPa

Traffic gr1a Footway - for Bending design 1 Loading

MA p p l i e d = 19.32731 kN.m PA p p l i e d = 1.418796 kN Corresponding stresses: top stress = 1.418796/905051.1 + 19.32731/5.8116E8 = 0.00157 + 0.03326 = 0.03482 MPa bottom stress = 1.418796/905051.1 + 19.32731/-2.586E8 = 0.00157 + -0.075 = -0.0732 MPa

TOTAL LOSS OF PRESTRESS SUMMARY Initial stressing force Prestress after all losses at t = ∞

= 4448.25 kN = 3142.75 kN

Corresponding loss = 29.3 %

LIMITING STRESSES IN PRECAST BEAM Compression EN 1992-2 Clause 7.2(102) k1 .fc k = 0.6*40.0 = 24.0 MPa In the presence of confinement or increase in cover this may be increased by up to 10%, i.e to: = 26.4 MPa

SAM v6.50d

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

84

Page: 10

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Tension Tension is governed by crack width considerations, and reinforcement provided for crack width control. Exposure Class is XD1, XD2, XD3, XS1, XS2, XS3 ... ... for which decompression is checked for the Frequent combination of loads. Decompression requires all of the tendon to be at least 65.0 mm above the level of the neutral axis.

LIMITING STRESSES FOR IN SITU CONCRETE Compression EN 1992-2-2 Clause 7.2(102) To avoid longitudinal cracking, compressive stress is limited to: σc = k1 .fc k = 0.6*31.875 = 19.125 MPa Tension Tension is governed by crack width considerations, and reinforcement provided for crack width control. EN 1992-1_1 Clause 7.3 However, no tensile stress is present at this section.

TRANSMISSION LENGTH Bond stress at release, EN 1992-1-1 Clause 8.10.2.2(1) fb p t = ηp 1 .η1 .fc t d (t) where fc t d (t) = αc t .0.7fc t m (t)/γc fc t m (t) = -2.3253 MPa αc t = 1.0

[2]

- from EN 1992-1-1/3.1.6(2)

tendon type coefficient, bond condition coefficient, hence

Expression (8.15)

ηp 1 = η1 =

3.2 1.0

fc t d (t) = 1.0*0.7*-2.3253/1.5 = -1.0851 MPa

and

fb p t = 3.2*1.0*-1.0851 = -3.4724 MPa

SAM v6.50d

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

85

Page: 11

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Basic transmission length, EN 1992-1-1 Clause 8.10.2.2(2) lp t = α1 .α2 .φ.σp m 0 /fb p t where speed of release coefficient, tendon surface coefficient, nominal diameter of tendon, tendon stress after release,

hence

Expression (8.16)

α1 = α2 = φ = σp m 0 =

1.0 0.19 16.0 mm 1440.0 MPa

lp t = 1.0*0.19*16.0*1440.0 / 3.47242 = 1.26068 m

Design value of transmission length, EN 1992-1-1 Clause 8.10.2.2(3) lp t 1 = 0.8*lp t = 0.8*1.26068 = 1.00854 m

STRUCTURAL EFFECTS OF TIME DEPENDENT BEHAVIOUR EN 1992-2 Annex KK.7 Age of concrete at first loading, Age of concrete when first composite, Age of concrete at time considered, Creep coefficient when first composite, Final creep coefficient, Creep coefficient increment, Specified value of Ageing coefficient,

t0 = 4.0 days tc = 60.0 days t = ∞ φ(tc ,t0 ) = 0.89250 φ(∞,t0 ) = 2.00881 φ(∞,tc ) = 1.20422 χ = 0.8

From Expression (KK.119): φ(∞,t0 ) - φ(tc ,t0 ) 2.00881-0.89250 ————————————————— = ————————————————————— 1 + χ.φ(∞,tc ) 1.0 + 0.8*1.20422 = 0.56856

SAM v6.50d

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

86

Page: 12

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

SLS STRESS SUMMARY TABLE Concrete Stresses (MPa)

 

force kN

 

 

moment kN.m

In situ top bottom

Precast top bottom

CHARACTERISTIC PERMANENT ACTIONS AND PRESTRESS [3]

Prestress

4244.91

Self Weight

-1547.7

-4.1499

17.4906

740.364

5.76481

-4.5869

—————————————————————————————————————————————————————— Prestress + Self Weight Elastic Def  

-203.96

TRANSFER

90.6953

1.61496

12.9036

0.32653

-0.9415

4040.95

-716.68

1.94149

11.9621

-257.14

176.251

0.89371

-1.5706

Erection

-2.3584

-0.0184

0.01461

In situ 1A

512.315

3.98911

-3.174

Cr+Sh+Rlx

B

In situ 1B

21.8745 0.0

0.05072

0.03293

0.03764

-0.0846

0.0

0.0

0.0

0.0

6.8436

7.14742

TOTAL PERMANENT EFFECTS, S0

 

Cr+Sh+Rlx

A

-641.05

439.384

TOTAL PERMANENT EFFECTS, S0 , ∞

 

0.34886

-0.0084

0.04774

-2.4076

0.39958

0.0245

6.89134

4.73984

CREEP REDISTRIBUTION according to EN 1992-2 Annex KK.7 Construction On Centering, Sc = G + P1 + P2 Permanent G

606.626

1.40663

0.91333

1.04381

-2.3461

Prestress P1

-2584.1

-5.992

-3.8906

-4.4465

9.99388

3.95141

3.95141

4.17748

4.17748

5.40251

3.50787

4.00902

-9.0107

2.68239

2.52957

-1.1711

-2.4635

3.08198

2.55407

5.72024

2.27635

99.6592

0.23108

0.15004

0.17148

-0.3854

286.182

-0.2604

-0.4932

1.16132

-0.4378

-101.97

-0.2364

-0.1535

-0.1754

0.39436

5.89172 6.87758

1.89092 1.8474]

3780.83

Prestress P2

2329.9

(Sc - S0 )*0.56856 Hence from KK.119, TOTAL CONSTRUCTION EFFECTS, S∞

[4]

[5]

 

 

SDL Diff. Shr. 1

605.383

Diff. Shr. 2

[Differential shrinkage is included when adverse TOTAL PERMANENT EFFECTS [including diff. shrinkage

 

 

SAM v6.50d

3.31306 2.81612

2.70412 2.05738

]

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

87

Page: 13

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

VARIABLE ACTIONS - CHARACTERISTIC COMBINATION Traffic Selected case: Traffic gr1a TS

1

934.303

-43.822 Traffic gr1a UDL 1

324.407

-4.3657 Traffic gr1a FT

1

19.3273

1.4188

2.16644

1.40668

1.60764

-3.6133

-0.0458

-0.0458

-0.0484

-0.0484

0.75222

0.48842

0.55820

-1.2546

-0.0046

-0.0046

-0.0048

-0.0048

0.04482

0.0291

0.03326

-0.0747

0.00148

0.00148

0.00157

0.00157

Total (Leading)

:

2.9146

1.87532

2.14742

-4.9944

Total (in Combination)

: 2.16974

1.39579

1.59838

-3.7202

-0.2524

-0.2885

0.64854

ψ0

0.75 0.75 0.4

Other traffic cases for comparison: Traffic gr1a TS

2

-167.69

-0.3888 0.0147

0.0147

0.01554

0.01554

-89.68

-0.2079

-0.1350

-0.1543

0.34682

0.00546

0.00546

0.00577

0.00577

0.04482

0.0291

0.03326

-0.0747

0.00148

0.00148

0.00157

0.00157

Total (Leading)

: -0.5303

-0.3367

-0.3867

0.94350

Total (in Combination)

: -0.4139

-0.2632

-0.3022

0.73324

14.063 Traffic gr1a UDL 2 5.225 Traffic gr1a FT

2

19.3273

1.4188

0.75 0.75 0.4

Temperature Restraint None defined Differential Temperature - Heating Diff. Tmp H1

-1016.0

Diff. Tmp H2

-413.84

2.47603

-0.8853

-0.8625

1.35841

285.183

0.66127

0.42936

0.49071

-1.1029

0.6

Differential Temperature - Cooling Diff. Tmp C1

976.559

Diff. Tmp C2

143.384

-1.4373

0.52916

0.24758

-1.7606

-98.811

-0.2291

-0.1487

-0.1700

0.38214

0.6

Other Variable Action None defined The following combinations of variable actions are evaluated in accordance with EN 1990 Equation 6.14b: a) Traffic as leading action + ψ0(Thermal + Other) b) Thermal as leading action + ψ0(Traffic + Other) c) Other as leading action + ψ0(Traffic + Thermal) For thermal actions the following cases are considered: i) temperature restraint alone ii) differential temperature: Heating iii) differential temperature: Cooling iv) temperature restraint + differential temperature: Heating v) temperature restraint + differential temperature: Cooling

SAM v6.50d

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

88

Page: 14

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

The most adverse case is with Traffic as leading action

Traffic ψ0 x Thermal

2.9146

1.87532

2.14742

-4.9944

1.88238

-0.2735

0.04654

-0.8270

0.0

0.0

0.0

0.0

ψ0 x Other  

 

TOTAL VARIABLE ACTIONS TOTAL PERMANENT (from above)

 

 

TOTAL COMBINATION

4.79698 1.60173 2.19396 -5.8215 3.31306 2.70412 6.87758 1.8474 —————————————————————————————————— 8.11005 4.30585 9.07154 -3.9741

WARNING - The flexural tensile stress exceeds the value of fct,eff so the section cannot be assumed to be uncracked. (EN 1992-1-1/7.1(2)) A cracked section analysis must be performed to derive the true compression stress in the concrete.

VARIABLE ACTIONS - FREQUENT COMBINATION Traffic Selected case:

ψ2

ψ1 = 0.75

Traffic gr1a TS

1

700.727

-32.867 ψ1 = 0.75

Traffic gr1a UDL 1

243.305

-3.2743 ψ1 =

1.62483

1.05501

1.20573

-2.71

-0.0343

-0.0343

-0.0363

-0.0363

0.56417

0.36631

0.41865

-0.9409

-0.0034

-0.0034

-0.0036

-0.0036

0.0

0.0

0.4

however, EN 1991-2 Clause 4.5.2 excludes the footway loading from the frequent action of LM1 Traffic gr1a FT

1

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Total (Leading)

: 2.15123

Total (in Combination)

:

0.0

1.38355

1.58445

-3.6909

0.0

0.0

0.0

0.0

-0.2916

-0.1893

-0.2164

0.48640

0.01102

0.01102

0.01165

0.01165

-0.1559

-0.1012

-0.1157

0.26012

0.0041

0.0041

0.00433

0.00433

0.0

Other traffic cases for comparison: ψ1 = 0.75

Traffic gr1a TS

2

-125.77

10.5473 ψ1 = 0.75

Traffic gr1a UDL 2

-67.26

3.91875 ψ1 =

0.0

0.0

0.4

however, EN 1991-2 Clause 4.5.2 excludes the footway loading from the frequent action of LM1 Traffic gr1a FT

2

0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Total (Leading)

: -0.4324

-0.2755

-0.3161

0.76251

Total (in Combination)

:

0.0

0.0

0.0

0.0

0.0

Temperature Restraint None defined SAM v6.50d

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

89

Page: 15

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Differential Temperature - Heating ψ1 =

0.6

Diff. Tmp H1

-1016.0

Diff. Tmp H2

-413.84

2.47603

-0.8853

-0.8625

1.35841

285.183

0.66127

0.42936

0.49071

-1.1029

0.5

Differential Temperature - Cooling ψ1 =

0.6

Diff. Tmp C1

976.559

Diff. Tmp C2

143.384

-1.4373

0.52916

0.24758

-1.7606

-98.811

-0.2291

-0.1487

-0.1700

0.38214

0.5

Other Variable Action None defined The following combinations of variable actions are evaluated in accordance with EN 1990 Equation 6.15b: a) ψ1(Traffic) as leading action + ψ2(Thermal + Other) b) ψ1(Thermal) as leading action + ψ2(Traffic + Other) c) ψ1(Other) as leading action + ψ2(Traffic + Thermal) For thermal actions the following cases are considered: i) temperature restraint alone ii) differential temperature: Heating iii) differential temperature: Cooling iv) temperature restraint + differential temperature: Heating v) temperature restraint + differential temperature: Cooling The most adverse case is with Traffic as leading action

ψ1 x Traffic ψ2 x Thermal ψ2 x Other  

 

TOTAL VARIABLE ACTIONS TOTAL PERMANENT (from above)

 

 

TOTAL COMBINATION

2.15123

1.38355

1.58445

-3.6909

1.56865

-0.2279

0.03878

-0.6892

0.0

0.0

0.0

0.0

3.71988 1.15556 1.62323 -4.3801 3.31306 2.70412 6.87758 1.8474 —————————————————————————————————— 7.03294 3.85968 8.50081 -2.5327

SLS FLEXURE Precast

 

Stress

 

(MPa)

 

After Transfer

After Erection

SAM v6.50d

T B

T B

E

Strain -6

Curvature -6

(x10 )

Deflection (mm)

(x10 )

(rad/m)

Here

1.94149 ET 62.3657

-247.61

15.0561

15.0561

-314.42

19.6107

19.6107

11.9621

384.253

2.81685 EI 151.712 10.4061

Max.

560.458

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

90

Page: 16

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

After in situ 1A After in situ 1B

Long-term Dead

Diff. Temp H1 Diff. Temp H2 Diff. Temp C1 Diff. Temp C2

Traffic gr1a 1

T B T B

T B

T B T B T B T B

T B

6.80596 EI 366.561 7.23201 6.8436 7.14742

EI 368.588

245.625

-4.8888

-4.8888

-29.104

1.59073

1.59073

20.8834

-1.1442

-1.1726

26.3161

-1.4413

-1.4413

-7.2357

0.39644

0.40625

155.98

-6.7548

-6.7548

420.685

-12.688

-12.688

-29.993 6.51001

2.14742 ES 60.9709 -4.9944

5.84195

-18.789

-0.1020 ES -2.8964 0.22928

5.84195

23.1413

0.14855 ES 4.2178 -1.0564

-12.587

368.27

0.29442 ES 8.35951 -0.6617

6.14087

384.951

-0.5175 ES -14.695 0.81504

6.14087

389.507

8.04868 EL 687.582 4.31089

-17.651

-141.8

Extreme in-service

Curvatures here are derived from precast section height: 1300.0mm ET = Elastic Modulus at Transfer = 31130.7MPa [EN1992-1-1 Clauses 3.1.3-(3) and 3.1.2-(6) with age 4 days] EI = Intermediate Term Elastic Modulus = 18567.1MPa [EN1992-1-1 Clause 7.4.3-(5) at 60.0 days (φ=0.89693)] EL = Long Term Elastic Modulus = 11705.8MPa [EN1992-1-1 Clause 7.4.3-(5) at infinite time (φ=2.00881)] ES = Short Term Elastic Modulus [Ecm]

= 35220.5MPa

________ [1] Refer to EN 1991-1-1 Table A.1 Note 1) [2] For the derivation of this value refer to the limiting stress calculations for transfer [3] includes draw-in and initial relaxation [4] With immediate losses and shrinkage / creep / relaxation losses until time at which insitu is cast. [5] Secondary effects arising from prestress in continuous section.

SAM v6.50d

06/02/2012 10:09:59

© 2012 Bestech Systems Ltd

91

Page: 17

92

Pre-tensioned Pre-stressed Beam Bridge Design Example

13.

Verification: ULS Bending - Mid Span

93

94

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design code: EN 1992-2:2005 with UK National Annex (modified) EN 1990 Equation 6.10 ULS Persistent / Transient Load case: Traffic gr1a TS - for Bending design 1 Section Ref 1 at 10.5m from left end of beam

Section details:

Ref 1 "Section 1" at 0.5 x span = 10.5 m from left end of beam

Analysis:

Traffic Actions: Bending for gr1a, loading I.D. 1 Ultimate Limit State: Persistent / Transient - EN 1990 Equation 6.10

ULS Stress / Strain summary for section with HOGGING moment  

Location

strain

 

Precast beam

height mm

-0.02234

0.0

0.0035

22.6667

0.0

-0.025719

0.0

1470.0

- bottom -0.021744

0.0

1270.0

-0.025441

-1391.3

1200.0

- bottom -0.002627

-512.29

60.0

- top - bottom

In situ stage 1 - top Tendon

stress MPa

- top

1300.0

Resistance of section = -551.202 kN.m In conjunction with axial load of -48.0244 kN

SAM v6.50d

06/02/2012 10:13:14

© 2012 Bestech Systems Ltd

95

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

ULS Stress / Strain summary for section with SAGGING moment  

Location

strain

 

Precast beam

- top

-5.156E-4

- bottom -0.031223

height mm

0.0

1300.0

0.0

0.0

18.0625

1470.0

- bottom -0.001224

0.0

1270.0

-0.007966

-1391.3

1200.0

-0.03474

-1391.3

60.0

In situ stage 1 - top Tendon

stress MPa

- top - bottom

0.0035

Resistance of section = 5221.3 kN.m In conjunction with axial load of -48.0244 kN

TRANSMISSION and ANCHORAGE Bond stress at release, EN 1992-1-1 Clause 8.10.2.2(1) fb p t = ηp 1 .η1 .fc t d (t) where fc t d (t) = αc t .0.7fc t m (t)/γc fc t m (t) = -2.3253 MPa αc t = 1.0

[1]

- from EN 1992-1-1/3.1.6(2)

tendon type coefficient, bond condition coefficient, hence

Expression (8.15)

ηp 1 = η1 =

3.2 1.0

fc t d (t) = 1.0*0.7*-2.3253/1.5 = -1.0851 MPa

and

fb p t = 3.2*1.0*-1.0851 = -3.4724 MPa

Basic transmission length, EN 1992-1-1 Clause 8.10.2.2(2) lp t = α1 .α2 .φ.σp m 0 /fb p t where speed of release coefficient, tendon surface coefficient, nominal diameter of tendon, tendon stress after release,

hence

Expression (8.16)

α1 = α2 = φ = σp m 0 =

1.0 0.19 16.0 mm 1440.0 MPa

lp t = 1.0*0.19*16.0*1440.0 / 3.47242 = 1.26068 m

SAM v6.50d

06/02/2012 10:13:14

© 2012 Bestech Systems Ltd

96

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design value of transmission length, EN 1992-1-1 Clause 8.10.2.2(3) lp t 2 = 1.2*lp t = 1.2*1.26068 = 1.51281 m

Anchorage of the tendons for the ultimate limit state: Bond stress for anchorage EN 1992-1-1 Clause 8.10.2.3(2) where

fb p d = ηp 2 .η1 .fc t d

Expression (8.20)

fc t d = αc t .0.7fc t m /γc = 1.0*0.7*-3.5088/1.5 = -1.6374 MPa

tendon type coefficient, hence

ηp 2 = 1.2

fb p d = 1.2*1.0*-1.6374 = -1.9649 MPa

Total anchorage length, EN 1992-1-1 Clause 8.10.2.3(4) lb p d = lp t 2 + α2 .φ.(σp d -σp m ∞ )/fb p d

For a tendon stressed to its limit, stress in tendon,

σp d = -1391.3 MPa

[2]

prestress after all losses, hence

Expression (8.21)

σp m ∞ = -1069.1 MPa

lb p d = 1.51281 + 0.19*16.0*(-1391.3--1069.1)/-1.9649 = 2.01123 m

SUMMARY OF ACTIONS PERMANENT ACTIONS  

ACTION TYPE

MOMENT kN.m

 

 

AXIAL kN

Beam erection before composite

=

996.3078

0.0

Construction stage 1A

=

691.6251

0.0

Construction stage 1B

=

29.53059

0.0

Surfacing

=

119.591

0.0

Differential Shrinkage / creep

=

0.0

0.0

1837.0545

0.0

TOTAL PERMANENT ACTIONS,

SAM v6.50d

γG x Gk

06/02/2012 10:13:14

© 2012 Bestech Systems Ltd

97

[3]

Page: 3

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

VARIABLE ACTIONS  

ACTION TYPE

MOMENT kN.m

Differential Temperature - Heating =

442.0334

 

AXIAL kN 0.0

Differential Temperature - Cooling = -153.1568

0.0

ψ0

ψ1

ψ2

0.6

0.6

0.5

0.6

0.6

0.5

Traffic gr1a TS - for Bending desi =

1261.308

-59.16024

0.75 0.75

0.0

Traffic gr1a UDL - for Bending des =

437.9499

-5.893762

0.75 0.75

0.0

Traffic gr1a Footway - for Bending =

26.09187

1.915374

0.4

0.4

0.0

TOTAL VARIABLE ACTIONS, γQ , 1 x Qk , 1 "+" ΣγQ , i x ψ0 x Qk , i TOTAL VARIABLE ACTIONS, Qk , 1 "+" Σψ0 x Qk , i [4]

Thermal effects are set to zero when not adverse. Traffic leading:

Traffic

1725.3498

-63.13863

0.0

0.0

0.0

0.0

Total

1725.3498

-63.13863

ψ0 x Traffic

1284.8802

-48.02435

442.0334

0.0

0.0

0.0

ψ0 x Thermal ψ0 x Other  

Thermal leading:

Thermal

ψ0 x Other  

Other leading:

Total

1726.9136

-48.02435

ψ0 x Traffic

1284.8802

-48.02435

ψ0 x Thermal

 

0.0

0.0

Other

0.0

0.0

Total

1284.8802

-48.02435

Critical case is with thermal leading

TOTAL COMBINATION

———————————————————————— 3563.9681 -48.02435

________ [1] For the derivation of this value refer to the limiting stress calculations for transfer [2] Typical value used - varies for each tendon [3] Shrinkage effects are excluded at ULS in accordance with EN1992-1-1/2.3.2.2(2) [4] When thermal effects are not adverse, they are excluded at ULS according to EN 1992-1-1/2.3.1.2

SAM v6.50d

06/02/2012 10:13:14

© 2012 Bestech Systems Ltd

98

Page: 4

Pre-tensioned Pre-stressed Beam Bridge Design Example

14.

Verification: SLS bending – Pier

99

100

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design code:

EN 1992-2:2005 with UK National Annex (modified) EN 1990 Equation 6.14 SLS Characteristic Exposure Class: XD1, XD2, XS1, XS2, XS3 Load case: Traffic gr1a TS - for Bending design 1 Section Ref 2 at 21m from left end of beam

WARNING - A reduction of flange width to allow for shear lag effects may be appropriate for this beam. SAM makes no allowance for this. Refer to EN 1992-1-1/5.3.2.1

Section details:

Ref 2 "Section 2" at 1 x span = 21 m from left end of beam

Analysis:

Traffic Actions: Bending for gr1a, loading I.D. 1 At time considered, t = ∞ Serviceability Limit State: Characteristic - EN 1990 Equation 6.14

ACTUAL STRESSES IN PRECAST BEAM No. No. No. No.

of tendons fully bonded at this section: 0 of tendons fully debonded at this section: 7 of tendons deflected at this section: 0 of tendons partially stressed: 14 (i.e. within the transmission length) The prestress force in these tendons is interpolated in accordance with EN 1992-1-1 clause 8.10.2.2.

SAM v6.50d

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

101

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Maximum Stressing Force - EN 1992-1-1 Clause 5.10.2.1(1)P For tendon property Grade 1600 Ep 195.0 k1 .fp k = 0.8*1860.0 = 1488.0 MPa k2 .fp 0 , 1 k = 0.9*1600.0 = 1440.0 MPa Wedge draw-in loss Clause 5.10.4(1)(i) draw-in strain = 0.003/21.0 = 1.43E-4 loss = Ep . strain = 195.0*1.43E-4 = 27.8571 MPa Heat Curing Clause 5.10.4(1)(ii)(Note) Concrete is cured at ambient temperature

Immediate Losses - EN 1992-1-1 Clause 5.10.4  

 

 

height No of mm tendons TOTAL

fp MPa

k1 /k2

draw-in MPa

heat cure MPa

area mm²

initial force kN

0

0.0

In accordance with clause 5.10.9(1), for SLS, the Characteristic value must be used. With ri n f = 1.0, Pk , i n f = 0.0 kN

Friction Clause 5.10.4(1)(i)

All tendons are straight in this beam.

Initial Relaxation Clause 5.10.4(1)(ii)

Loss is calculated from clause 3.3.2(7) For tendon property Grade 1600 Ep 195.0 relaxation loss at 1000 hours, ρ1 0 0 0 = 8.0 % μ = σp i / fp k = 0.0-0.0-0.0/1860.0 = 0.0 time after tensioning = 96.0 hours for Class 1 relaxation, use Expression (3.28) 6.7μ

5.39 . ρ1 0 0 0 . e

0.75(1-μ)

. [t/1000]

= 5.39 * 8.0 * 1.0 * 0.17246 * 10 = 7.44E-5 relaxation

 

 

 

 

-5

height No of mm tendons TOTAL

area x σp i

%

. 10

-5

After relaxation loss kN

force kN

0

SAM v6.50d

0.0

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

102

moment kN.m 0.0

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Moment about the centroid of the precast beam: Mr = 0.0-(0.0*0.5760392) = 0.0 kN.m Corresponding stresses: top stress = 0.0/537225.68+0.0/1.2843E8 = 0.0+0.0 = 0.0 MPa bottom stress = 0.0/537225.68+0.0/-1.614E8 = 0.0+0.0 = 0.0 MPa Self weight moment: c.s.a. = 5.372E5 mm²

[1]

density = 24.0 kN/m³ + 1.0 kN/m³ = 25.0 kN/m³ self weight = 5.372E5*25.0 = 13.4306 kN/m beam length = 21.0 m distance = 21.0 m Ms w = 0.5*13.4306*21.0*(21.0-21.0) = 0.0 kN.m Corresponding stresses: top stress = 0.0/1.2843E8 = 0.0 MPa bottom stress = 0.0/-1.614E8 = 0.0 MPa

Elastic Deformation - Clause 5.10.4(1)(iii) stress at top of precast beam stress at bottom of precast beam depth of precast beam elastic modulus of concrete at transfer

 

height

 

 

 

mm TOTAL

No of tendons 0

conc stress MPa

conc strain

= 0.0 = 0.0 = 1300.0 = 31.1307

tendon force kN

MPa MPa mm GPa

tendon moment kN.m 0.0

0.0

Moment about the centroid of the precast beam: Me d = 0.0-(0.0*0.5760392) = 0.0 kN.m hence, top stress = 0.0-0.0/537.22568-0.0/1.2843E8 = 0.0-0.0-0.0 = 0.0 MPa bottom stress = 0.0-0.0/537.22568-0.0/-1.614E8 = 0.0-0.0-0.0 = 0.0 MPa After a further 0 iterations of the above process, the top and bottom stresses are as follows: top stress = 0.0 MPa bottom stress = 0.0 MPa

SAM v6.50d

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

103

Page: 3

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Max Prestress Force after transfer - EN 1992-1-1 Clause 5.10.3.(2) For tendon property Grade 1600 Ep 195.0 k7 .fp k = 0.75*1860.0 = 1395.0 MPa k8 .fp 0 , 1 k = 0.85*1600.0 = 1360.0 MPa Maximum tendon stress after transfer = 1272.24 MPa which is not greater than 1360.0 and therefore OK.

ACTIONS DURING EXECUTION Erection of beam Loading

Bending moment from erection loadcase at current span location: MA p p l i e d = 0.0 kN.m Corresponding stresses: top stress = 0.0/1.2843E8 = 0.0 MPa bottom stress = 0.0/-1.614E8 = 0.0 MPa Remove the dead load applied for transfer calculations Ms w = 0.0 kN.m Corresponding stresses: top stress = 0.0/1.2843E8 = 0.0 MPa bottom stress = 0.0/-1.614E8 = 0.0 MPa

Time Dependent Losses - EN 1992-1-1 Clause 5.10.6 Simplified method using Expression (5.46) ΔPc + s + r = Ap .Δσp , c + s + r εc s .Ep + 0.8Δσp r + Ep /Ec m .φ(t,t0 ).σc , Q P Δσp , c + s + r = —————————————————————————————————————————————— 1 + Ep /Ec m .Ap /Ac (1+Ac /Ic .zc p ²)[1+0.8φ(t,t0 )] The calculated loss is apportioned partly to the precast beam alone and partly to the full composite section. For in-situ cast at 60 days, the proportion of the loss occurring before the in-situ is cast is calculated to be 30.0 %

SAM v6.50d

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

104

Page: 4

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Losses are calculated for time t = ∞ Age of concrete at end of curing, Age of concrete at transfer,

ts = t0 =

1.0 days 4.0 days

Age is adjusted for expression (B.5) (for cement type & temperature) - for cement class N (α = 0) 1.2

α

adjusted t0 = t0 , T . [(9/(2+t0 , T )+1) >=0.5 Expression (B.9) 1.2 0 = 4.0 * [(9/(2+4.0 )+1] = 4.0 days Age of concrete at time considered, t = ∞ EN 1992-1-1/3.3.2(8) for relaxation, t is taken as 500,000 hours Concrete age coefficient (Expression (3.2)), βcc: βc c ( t ) = fc m ( t ) /fc m Expression (3.1) = exp{s[1-√(28/t)]} Expression (3.2) Coefficient for Class N cement, s = 0.25 βc c ( t 0 ) = exp{0.25[1.0-√(28/4.0)]} = 0.66269 βc c ( t ) = exp{0.25} = 1.28403 Characteristic strength of concrete, fc k = 40.0 MPa Mean compressive strength of concrete, fc m = 40.0 + 8.0 (from Table 3.1) = 48.0 MPa fc m 0 = 10.0 MPa fc m ( t 0 ) = βc c ( t 0 ) . fc m = 31.8094 MPa Ambient relative humidity = 80.0 % Notional size of member, h0 = 2Ac /u = 2*9.283E5/7245.89 = 256.223 mm Modulus of elasticity of concrete at 28 days, Ec m = 35.2205 GPa Modulus of elasticity of concrete at time considered, Ec m ( t ) = βc c ( t )

0.3

Expressions (3.5) & (3.1)

. Ec m

0.3

= 1.28403 * 35.2205 = 37.9636 GPa

Area of concrete cross section, Ac = 9.28E5 mm² Perimeter of concrete cross section, u = 7245.9 mm Notional size, h0 = 2*Ac /u = 2*9.283E5/7245.89 = 256.22 mm

Creep coefficient for concrete - EN 1992-1-1 clause 3.1.4 and Annex B.1 φ(t,t0 ) = φ0 . βc (t,t0 ) = φR H . β(fc m ) . β(t0 ) . βc (t,t0 )

SAM v6.50d

Expression (B.1) Expression (B.2)

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

105

Page: 5

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

for fc m >

35.0 MPa 1-RH/100 φR H = [ 1 + ——————————— . α1 ] .α2 0.33 0.1*h0 α1 = [35.0/48.0] α2 = [35.0/48.0] α3 = [35.0/48.0]

0.7 0.2 0.5

Expression (B.3b)

= 0.80163 = 0.93878 = 0.85391

φR H = [1.0 + (1.0-0.8) / (0.1*256.223 = 1.17576

0.33

) * 0.80163]*0.93878

β(fc m ) = 16.8/√fc m = 16.8/√48.0 = 2.42487

Expression (B.4)

For Permanent Loads

In the absence of heat curing t0 , T = 4.0 days age is adjusted for expression (B.5) (for cement type and temperature) - for cement class N (α = 0) 9.0

t0 = t0 , T . [ —————————————— + 1.0 ] 1.2 2.0 + t0 , T 9.0

= 4.0 =

α

* [ —————————————— + 1.0 ]

2.0 + 4.0 4.0 day

>=0.5

Expression (B.9)

0

1.2

0.2

β(t0 ) = 1/(0.1+t0 ) 0.2 = 1/(0.1+4.0 ) = 0.70446 βc (t,t0 ) = 1.0 for time t = ∞ hence from (B.1) and (B.2): φ(t,t0 ) = 1.17576*2.42487*0.70446 = 2.00849

Expression (B.5)

Check for creep non-linearity EN 1992-1-1 clause 3.1.4(4) At the level of the centroid of the tendons, the compressive stress in the concrete at time t0 = 0.0 MPa. This does not exceed 0.45*fck(t0), i.e. 18.0 MPa, so non-linear creep is not considered

Shrinkage Strain for concrete - EN 1992-1-1 clause 3.1.4(6) Total Shrinkage: εc s = εc d + εc a

SAM v6.50d

(3.8)

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

106

Page: 6

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Drying Shrinkage - Expression (3.9): εc d (t) = βd s (t,ts ).kh .εc d , 0 βd s (t,ts ) = 1.0 for t = ∞ From Table 3.3: kh = 0.79377 From Annex B, Expression (B.11):

-6

εc d , 0 = 0.85[(220+110.αd s 1 ).(exp(-αd s 2 .fc m /fc m 0 )].10 .βR H βR H = 1.55[1.0-(RH/100)³] (B.12) = 0.7564 For cement class N, αd s 1 = 4 αd s 2 = 0.12 hence, -6

εc d , 0 = 0.85[(220+110*4.0)*exp(-0.12*48.0/10.0)]*10 *0.7564 -6

and,

= 238.54*10

εc d (t) = 1.0*0.79377*238.54*10

-6

-6

= 189.347*10

Autogenous Shrinkage - Expression (3.11): εc a (t) = βa s (t).εc a (∞) βa s (t) = 1.0 for t = ∞ εc a (∞) = 2.5*(fc k -10.0)*10 -6 = 75.0*10 hence, εc a (t) = 1.0*75.0*10 = 75.0*10

-6

-6

-6

Total Shrinkage: εc s = εc d (t) + εc a (t) = 189.3473 + 75.0 -6

= 264.3473*10

Further Relaxation Clause 5.10.6(1)(b) Loss is calculated from clause 3.3.2(7) For tendon property Grade 1600 Ep 195.0 relaxation loss at 1000 hours, ρ1 0 0 0 = 8.0 % time after tensioning = 500000.0 hours μ = 0.75921 (as calculated for initial relaxation loss above) for Class 1 relaxation, use Expression (3.28) 6.7μ

5.39 . ρ1 0 0 0 . e

0.75(1-μ)

. [t/1000]

= 5.39 * 8.0 * 161.863 * 3.07185 * 10 = 0.21440

SAM v6.50d

-5

. 10

-5

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

107

Page: 7

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

With the initial relaxation deducted, the variation in tendon stress from relaxation becomes: Δσp r / σp i = 0.21440 - 0.04571 = 0.16868 Summary of the above for Expression (5.46):

Estimated shrinkage strain εc s Creep coefficient at t for loading at t0 φ(t,t0 ) Relaxation, Δσp r Modulus of elasticity for prestressing steel Ep Modulus of Elasticity for concrete Ec m Area of all prestressing Ap Area of concrete section Ac Second moment of area of concrete section Ic Ep /Ec m Ep /Ec m .Ap /Ac Ac /Ic

= 195.0/37.9636 = 5.1365*0.0/9.283E5 = 9.283E5/2.38E11

= = = = = = = =

264.347 2.00849 238.212 195.0 37.9636 0.0 9.283E5 2.38E11

-6

x10 MPa GPa GPa mm² mm² mm⁴

= 5.1365 = 0.0 = 3.89252

In the table below the following vary with tendon height: σc , Q P = Stress in concrete adjacent to tendons zc p = Section centre of gravity to tendons φ(t,t0 ) = Creep Coefficient (if non-linear creep is considered)  

 

height

 

 

mm

Ap mm²

shrink εc s .Ep MPa

relax 0.8Δσp r MPa

φ(t,t0 )

σc , Q P MPa

creep Ep /Ec m .φ.σ MPa

denom zc p mm

Total force loss: Total moment loss:

 

 

ΔPc + s + r kN 0.0 0.0

Mc s r = 0.0-(0.0*0.9124128) = 0.0 kN.m

Corresponding stresses - before composite: top stress = ( 0.0/5.372E5+0.0/1.284E8 )* 0.3 = ( 0.0+0.0 )* 0.3 = 0.0 MPa bottom stress = ( 0.0/5.372E5+0.0/-1.61E8 )* 0.3 = ( 0.0+0.0 )* 0.3 = 0.0 MPa top stress bottom stress

SAM v6.50d

= = = = = =

- after composite: ( 0.0/9.283E5+0.0/6.153E8 )*(1.0- 0.3) ( 0.0+0.0 )*(1.0-0.3) 0.0 MPa ( 0.0/9.283E5+0.0/-2.61E8 )*(1.0-0.3 ) ( 0.0+0.0 )*(1.0-0.3) 0.0 MPa

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

108

Page: 8

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Surfacing 1 Loading

MA p p l i e d = -130.6559 kN.m Corresponding stresses: top stress = -130.6559/6.1529E8 = -0.2123 MPa bottom stress = -130.6559/-2.614E8 = 0.49988 MPa

TOTAL LOSS OF PRESTRESS SUMMARY Initial stressing force Prestress after all losses at t = ∞

= =

0.0 kN 0.0 kN

Corresponding loss = 100 %

LIMITING STRESSES IN PRECAST BEAM Compression EN 1992-2 Clause 7.2(102) k1 .fc k = 0.6*40.0 = 24.0 MPa In the presence of confinement or increase in cover this may be increased by up to 10%, i.e to: = 26.4 MPa Tension Tension is governed by crack width considerations, and reinforcement provided for crack width control. Exposure Class is XD1, XD2, XD3, XS1, XS2, XS3 ... ... for which decompression is checked for the Frequent combination of loads. Decompression requires all of the tendon to be at least 65.0 mm above the level of the neutral axis.

LIMITING STRESSES FOR IN SITU CONCRETE Compression EN 1992-2-2 Clause 7.2(102) To avoid longitudinal cracking, compressive stress is limited to: σc = k1 .fc k = 0.6*31.875 = 19.125 MPa Tension Tension is governed by crack width considerations, and reinforcement provided for crack width control. EN 1992-1_1 Clause 7.3 However, no tensile stress is present at this section.

SAM v6.50d

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

109

Page: 9

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

TRANSMISSION LENGTH Bond stress at release, EN 1992-1-1 Clause 8.10.2.2(1) fb p t = ηp 1 .η1 .fc t d (t) where fc t d (t) = αc t .0.7fc t m (t)/γc fc t m (t) = -2.3253 MPa αc t = 1.0

[2]

- from EN 1992-1-1/3.1.6(2)

tendon type coefficient, bond condition coefficient, hence

Expression (8.15)

ηp 1 = η1 =

3.2 1.0

fc t d (t) = 1.0*0.7*-2.3253/1.5 = -1.0851 MPa

and

fb p t = 3.2*1.0*-1.0851 = -3.4724 MPa

Basic transmission length, EN 1992-1-1 Clause 8.10.2.2(2) lp t = α1 .α2 .φ.σp m 0 /fb p t where speed of release coefficient, tendon surface coefficient, nominal diameter of tendon, tendon stress after release,

hence

Expression (8.16)

α1 = α2 = φ = σp m 0 =

1.0 0.19 16.0 mm 1440.0 MPa

lp t = 1.0*0.19*16.0*1440.0 / 3.47242 = 1.26068 m

Design value of transmission length, EN 1992-1-1 Clause 8.10.2.2(3) lp t 1 = 0.8*lp t = 0.8*1.26068 = 1.00854 m

SAM v6.50d

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

110

Page: 10

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

STRUCTURAL EFFECTS OF TIME DEPENDENT BEHAVIOUR EN 1992-2 Annex KK.7 Age of concrete at first loading, Age of concrete when first composite, Age of concrete at time considered, Creep coefficient when first composite, Final creep coefficient, Creep coefficient increment, Specified value of Ageing coefficient,

t0 = 4.0 days tc = 60.0 days t = ∞ φ(tc ,t0 ) = 0.89250 φ(∞,t0 ) = 2.00881 φ(∞,tc ) = 1.20422 χ = 0.8

From Expression (KK.119): φ(∞,t0 ) - φ(tc ,t0 ) 2.00881-0.89250 ————————————————— = ————————————————————— 1 + χ.φ(∞,tc ) 1.0 + 0.8*1.20422 = 0.56856

SLS STRESS SUMMARY TABLE Concrete Stresses (MPa)

 

force kN

 

 

moment kN.m

In situ top bottom

Precast top bottom

CHARACTERISTIC PERMANENT ACTIONS AND PRESTRESS [3]

Prestress

0.0

Self Weight

0.0

0.0

0.0

0.0

0.0

0.0

—————————————————————————————————————————————————————— Prestress + Self Weight

 

0.0

0.0

Elastic Def

0.0

0.0

0.0

0.0

TRANSFER

0.0

0.0

0.0

0.0

0.0

Cr+Sh+Rlx

0.0

0.0

0.0

Erection

B

0.0

0.0

0.0

In situ 1A

0.0

0.0

0.0

In situ 1B

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0 TOTAL PERMANENT EFFECTS, S0

 

Cr+Sh+Rlx

A

0.0

0.0

TOTAL PERMANENT EFFECTS, S0 , ∞

 

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

CREEP REDISTRIBUTION according to EN 1992-2 Annex KK.7 Construction On Centering, Sc = G + P1 + P2 Permanent G

-1332.6

-2.9471

-1.89

-2.1658

5.09841

Prestress P1

0.0

0.0

0.0

0.0

0.0

Prestress P2

4659.29

10.3044

6.6083

7.57251

-17.826

SAM v6.50d

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

111

[4] [5]

Page: 11

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

(Sc - S0 )*0.56856

4.18309

2.68266

3.07408

-7.2366

4.18309

2.68266

3.07408

-7.2366

-130.66

-0.2889

-0.1853

-0.2123

0.49988

278.488

-0.3240

-0.5449

1.10477

-0.4133

-203.89

-0.4509

-0.2891

-0.3313

0.78006

2.86173 3.63513

-6.7368 -6.37]

Hence from KK.119, TOTAL CONSTRUCTION EFFECTS, S∞

 

 

SDL Diff. Shr. 1

605.383

Diff. Shr. 2

[Differential shrinkage is included when adverse TOTAL PERMANENT EFFECTS [including diff. shrinkage

3.89413 3.1192

 

 

2.49735 1.66324

]

VARIABLE ACTIONS - CHARACTERISTIC COMBINATION Traffic Selected case: Traffic gr1a TS

ψ0

1

0.0

0.0

0.0

0.0

0.0

0.75

Traffic gr1a UDL 1

0.0

0.0

0.0

0.0

0.0

0.75

Traffic gr1a FT

0.0

0.0

0.0

0.0

0.0

0.4

1

Total (Leading)

:

0.0

0.0

0.0

0.0

Total (in Combination)

:

0.0

0.0

0.0

0.0

-1.4342

-0.9197

-1.054

2.48113

0.13361

0.13361

0.14125

0.14125

-1.179

-0.7560

-0.8664

2.0396

0.07909

0.07909

0.08362

0.08362

-0.0769

-0.0493

-0.0565

0.13305

-0.0119

-0.0119

-0.0125

-0.0125

Total (Leading)

: -2.4892

-1.5243

-1.7646

4.86613

Total (in Combination)

: -1.8359

-1.1218

-1.2993

3.60741

Other traffic cases for comparison: Traffic gr1a TS

2

-648.5

131.125 Traffic gr1a UDL 2

-533.09

77.6189 Traffic gr1a FT

2

-34.778

-11.642

0.75 0.75 0.4

Temperature Restraint None defined Differential Temperature - Heating Diff. Tmp H1

-1016.0

Diff. Tmp H2

-400.93

2.57552

-0.8043

-0.7740

1.31996

570.322

1.26131

0.80889

0.92691

-2.182

0.6

Differential Temperature - Cooling Diff. Tmp C1

976.559

Diff. Tmp C2

130.974

-1.5057

0.47350

0.18673

-1.7342

-197.6

-0.4370

-0.2802

-0.3211

0.75602

0.6

Other Variable Action None defined

SAM v6.50d

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

112

Page: 12

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

The following combinations of variable actions are evaluated in accordance with EN 1990 Equation 6.14b: a) Traffic as leading action + ψ0(Thermal + Other) b) Thermal as leading action + ψ0(Traffic + Other) c) Other as leading action + ψ0(Traffic + Thermal) For thermal actions the following cases are considered: i) temperature restraint alone ii) differential temperature: Heating iii) differential temperature: Cooling iv) temperature restraint + differential temperature: Heating v) temperature restraint + differential temperature: Cooling The most adverse case is with Thermal (iii/v) as leading action

ψ0 x Traffic Thermal

0.0

0.0

0.0

0.0

-1.9427

0.19324

-0.1344

-0.9781

0.0

0.0

0.0

0.0

ψ0 x Other  

 

TOTAL VARIABLE ACTIONS TOTAL PERMANENT (from above)

 

 

TOTAL COMBINATION

-1.9427 0.19324 -0.1344 -0.9781 3.1192 2.49735 3.63513 -6.37 —————————————————————————————————— 1.1765 2.69059 3.50071 -7.3482

WARNING - The flexural tensile stress exceeds the value of fct,eff so the section cannot be assumed to be uncracked. (EN 1992-1-1/7.1(2)) A cracked section analysis must be performed to derive the true compression stress in the concrete.

VARIABLE ACTIONS - FREQUENT COMBINATION Traffic Selected case:

ψ2

ψ1 = 0.75

Traffic gr1a TS

1

0.0

0.0

0.0

0.0

0.0

0.0

Traffic gr1a UDL 1

0.0

0.0

0.0

0.0

0.0

0.0

ψ1 = 0.75 ψ1 =

0.4

however, EN 1991-2 Clause 4.5.2 excludes the footway loading from the frequent action of LM1 Traffic gr1a FT

0.0

0.0

0.0

0.0

Total (Leading)

1

0.0 :

0.0

0.0

0.0

0.0

Total (in Combination)

:

0.0

0.0

0.0

0.0

-1.0756

-0.6898

-0.7904

1.86085

0.10020

0.10020

0.10594

0.10594

-0.8842

-0.5670

-0.6498

1.5297

0.05932

0.05932

0.06271

0.06271

0.0

Other traffic cases for comparison: ψ1 = 0.75

Traffic gr1a TS

2

-486.37

98.3438 ψ1 = 0.75

Traffic gr1a UDL 2 58.2142 SAM v6.50d

-399.82

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

113

0.0

0.0

Page: 13

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

ψ1 =

0.4

however, EN 1991-2 Clause 4.5.2 excludes the footway loading from the frequent action of LM1 Traffic gr1a FT

2

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Total (Leading)

: -1.8004

-1.0974

-1.2716

3.55921

Total (in Combination)

:

0.0

0.0

0.0

0.0

-400.93

2.57552

-0.8043

-0.7740

1.31996

570.322

1.26131

0.80889

0.92691

-2.182

0.0

0.0

Temperature Restraint None defined Differential Temperature - Heating ψ1 =

0.6

Diff. Tmp H1

-1016.0

Diff. Tmp H2

0.5

Differential Temperature - Cooling ψ1 =

0.6

Diff. Tmp C1

976.559

Diff. Tmp C2

130.974

-1.5057

0.47350

0.18673

-1.7342

-197.6

-0.4370

-0.2802

-0.3211

0.75602

0.5

Other Variable Action None defined The following combinations of variable actions are evaluated in accordance with EN 1990 Equation 6.15b: a) ψ1(Traffic) as leading action + ψ2(Thermal + Other) b) ψ1(Thermal) as leading action + ψ2(Traffic + Other) c) ψ1(Other) as leading action + ψ2(Traffic + Thermal) For thermal actions the following cases are considered: i) temperature restraint alone ii) differential temperature: Heating iii) differential temperature: Cooling iv) temperature restraint + differential temperature: Heating v) temperature restraint + differential temperature: Cooling The most adverse case is with Thermal (iii/v) as leading action

ψ2 x Traffic ψ1 x Thermal ψ2 x Other  

 

TOTAL VARIABLE ACTIONS TOTAL PERMANENT (from above)

 

 

TOTAL COMBINATION

SAM v6.50d

0.0

0.0

0.0

0.0

-1.1656

0.11594

-0.0807

-0.5869

0.0

0.0

0.0

0.0

-1.1656 0.11594 -0.0807 -0.5869 3.1192 2.49735 3.63513 -6.7368 —————————————————————————————————— 1.95358 2.6133 3.55448 -7.3237

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

114

Page: 14

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

SLS FLEXURE Precast

 

Stress

 

(MPa)

 

After Transfer

After Erection

After in situ 1A After in situ 1B

Long-term Dead

Diff. Temp H1 Diff. Temp H2 Diff. Temp C1 Diff. Temp C2

Traffic gr1a 1 Extreme in-service

T B

T B

T B T B

T B

T B T B T B T B

T B

E

Strain -6

Curvature -6

(x10 )

Deflection (mm)

(x10 )

(rad/m)

Here

0.04918 ET 1.57982

2.16063

-4.E-16

15.0561

-33.436

1.7E-15

19.6107

-33.436

2.2E-16

6.14087

-32.586

-1.E-15

5.84195

-20.08

-2.E-16

-4.8888

-27.44

4.9E-16

1.59073

40.7406

1.9E-16

-1.1726

25.1724

-2.E-16

-1.4413

-14.116

-4.E-17

0.40625

-20.798

-2.E-15

-6.7548

-29.821

-3.E-15

-12.688

-0.0383

-1.229

-0.2764 EI -14.887 0.53063

28.5795

-0.2764 EI -14.887 0.53064

28.5797

-0.2649 EI -14.271 0.52154

28.0899

0.56105 EL 47.9295 0.86661

74.0333

-0.4644 ES -13.186 0.79197

22.4862

0.55615 ES 15.7905 -1.3092

-37.172

0.11203 ES 3.18107 -1.0405

-29.543

-0.1926 ES -5.471 0.45361

12.8793

-0.3085 ES -8.7613 0.64368

Max.

18.2758

Curvatures here are derived from precast section height: 1300.0mm ET = Elastic Modulus at Transfer = 31130.7MPa [EN1992-1-1 Clauses 3.1.3-(3) and 3.1.2-(6) with age 4 days] EI = Intermediate Term Elastic Modulus = 18567.1MPa [EN1992-1-1 Clause 7.4.3-(5) at 60.0 days (φ=0.89693)] EL = Long Term Elastic Modulus = 11705.8MPa [EN1992-1-1 Clause 7.4.3-(5) at infinite time (φ=2.00881)]

SAM v6.50d

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

115

Page: 15

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

ES = Short Term Elastic Modulus [Ecm]

= 35220.5MPa

________ [1] Refer to EN 1991-1-1 Table A.1 Note 1) [2] For the derivation of this value refer to the limiting stress calculations for transfer [3] includes draw-in and initial relaxation [4] With immediate losses and shrinkage / creep / relaxation losses until time at which insitu is cast. [5] Secondary effects arising from prestress in continuous section.

SAM v6.50d

03/02/2012 14:08:58

© 2012 Bestech Systems Ltd

116

Page: 16

Pre-tensioned Pre-stressed Beam Bridge Design Example

15.

Verification: SLS bending – Support

117

118

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design code:

EN 1992-2:2005 with UK National Annex (modified) EN 1990 Equation 6.14 SLS Characteristic Exposure Class: XD1, XD2, XS1, XS2, XS3 Load case: Traffic gr1a TS - for Bending design 1 Section Ref 1 at 0m from left end of beam

WARNING - A reduction of flange width to allow for shear lag effects may be appropriate for this beam. SAM makes no allowance for this. Refer to EN 1992-1-1/5.3.2.1

Section details:

Ref 1 "Section 1" at 0 x span = 0 m from left end of beam

Analysis:

Traffic Actions: Bending for gr1a, loading I.D. 1 At time considered, t = ∞ Serviceability Limit State: Characteristic - EN 1990 Equation 6.14

ACTUAL STRESSES IN PRECAST BEAM No. No. No. No.

of tendons fully bonded at this section: 0 of tendons fully debonded at this section: 7 of tendons deflected at this section: 0 of tendons partially stressed: 14 (i.e. within the transmission length) The prestress force in these tendons is interpolated in accordance with EN 1992-1-1 clause 8.10.2.2.

SAM v6.50d

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

119

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Maximum Stressing Force - EN 1992-1-1 Clause 5.10.2.1(1)P For tendon property Grade 1600 Ep 195.0 k1 .fp k = 0.8*1860.0 = 1488.0 MPa k2 .fp 0 , 1 k = 0.9*1600.0 = 1440.0 MPa Wedge draw-in loss Clause 5.10.4(1)(i) draw-in strain = 0.003/21.0 = 1.43E-4 loss = Ep . strain = 195.0*1.43E-4 = 27.8571 MPa Heat Curing Clause 5.10.4(1)(ii)(Note) Concrete is cured at ambient temperature

Immediate Losses - EN 1992-1-1 Clause 5.10.4  

 

 

height No of mm tendons TOTAL

fp MPa

k1 /k2

draw-in MPa

heat cure MPa

area mm²

initial force kN

0

0.0

In accordance with clause 5.10.9(1), for SLS, the Characteristic value must be used. With ri n f = 1.0, Pk , i n f = 0.0 kN

Friction Clause 5.10.4(1)(i)

All tendons are straight in this beam.

Initial Relaxation Clause 5.10.4(1)(ii)

Loss is calculated from clause 3.3.2(7) For tendon property Grade 1600 Ep 195.0 relaxation loss at 1000 hours, ρ1 0 0 0 = 8.0 % μ = σp i / fp k = 0.0-0.0-0.0/1860.0 = 0.0 time after tensioning = 96.0 hours for Class 1 relaxation, use Expression (3.28) 6.7μ

5.39 . ρ1 0 0 0 . e

0.75(1-μ)

. [t/1000]

= 5.39 * 8.0 * 1.0 * 0.17246 * 10 = 7.44E-5 relaxation

 

 

 

 

-5

height No of mm tendons TOTAL

area x σp i

%

. 10

-5

After relaxation loss kN

force kN

0

SAM v6.50d

0.0

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

120

moment kN.m 0.0

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Moment about the centroid of the precast beam: Mr = 0.0-(0.0*0.5760392) = 0.0 kN.m Corresponding stresses: top stress = 0.0/537225.68+0.0/1.2843E8 = 0.0+0.0 = 0.0 MPa bottom stress = 0.0/537225.68+0.0/-1.614E8 = 0.0+0.0 = 0.0 MPa Self weight moment: c.s.a. = 5.372E5 mm²

[1]

density = 24.0 kN/m³ + 1.0 kN/m³ = 25.0 kN/m³ self weight = 5.372E5*25.0 = 13.4306 kN/m beam length = 21.0 m distance = 0.0 m Ms w = 0.5*13.4306*0.0*(21.0-0.0) = 0.0 kN.m Corresponding stresses: top stress = 0.0/1.2843E8 = 0.0 MPa bottom stress = 0.0/-1.614E8 = 0.0 MPa

Elastic Deformation - Clause 5.10.4(1)(iii) stress at top of precast beam stress at bottom of precast beam depth of precast beam elastic modulus of concrete at transfer

 

height

 

 

 

mm TOTAL

No of tendons 0

conc stress MPa

conc strain

= 0.0 = 0.0 = 1300.0 = 31.1307

tendon force kN

MPa MPa mm GPa

tendon moment kN.m 0.0

0.0

Moment about the centroid of the precast beam: Me d = 0.0-(0.0*0.5760392) = 0.0 kN.m hence, top stress = 0.0-0.0/537.22568-0.0/1.2843E8 = 0.0-0.0-0.0 = 0.0 MPa bottom stress = 0.0-0.0/537.22568-0.0/-1.614E8 = 0.0-0.0-0.0 = 0.0 MPa After a further 0 iterations of the above process, the top and bottom stresses are as follows: top stress = 0.0 MPa bottom stress = 0.0 MPa

SAM v6.50d

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

121

Page: 3

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Max Prestress Force after transfer - EN 1992-1-1 Clause 5.10.3.(2) For tendon property Grade 1600 Ep 195.0 k7 .fp k = 0.75*1860.0 = 1395.0 MPa k8 .fp 0 , 1 k = 0.85*1600.0 = 1360.0 MPa Maximum tendon stress after transfer = 1272.24 MPa which is not greater than 1360.0 and therefore OK.

ACTIONS DURING EXECUTION Erection of beam Loading

Bending moment from erection loadcase at current span location: MA p p l i e d = 0.0 kN.m Corresponding stresses: top stress = 0.0/1.2843E8 = 0.0 MPa bottom stress = 0.0/-1.614E8 = 0.0 MPa Remove the dead load applied for transfer calculations Ms w = 0.0 kN.m Corresponding stresses: top stress = 0.0/1.2843E8 = 0.0 MPa bottom stress = 0.0/-1.614E8 = 0.0 MPa

Time Dependent Losses - EN 1992-1-1 Clause 5.10.6 Simplified method using Expression (5.46) ΔPc + s + r = Ap .Δσp , c + s + r εc s .Ep + 0.8Δσp r + Ep /Ec m .φ(t,t0 ).σc , Q P Δσp , c + s + r = —————————————————————————————————————————————— 1 + Ep /Ec m .Ap /Ac (1+Ac /Ic .zc p ²)[1+0.8φ(t,t0 )] The calculated loss is apportioned partly to the precast beam alone and partly to the full composite section. For in-situ cast at 60 days, the proportion of the loss occurring before the in-situ is cast is calculated to be 30.0 %

SAM v6.50d

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

122

Page: 4

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Losses are calculated for time t = ∞ Age of concrete at end of curing, Age of concrete at transfer,

ts = t0 =

1.0 days 4.0 days

Age is adjusted for expression (B.5) (for cement type & temperature) - for cement class N (α = 0) 1.2

α

adjusted t0 = t0 , T . [(9/(2+t0 , T )+1) >=0.5 Expression (B.9) 1.2 0 = 4.0 * [(9/(2+4.0 )+1] = 4.0 days Age of concrete at time considered, t = ∞ EN 1992-1-1/3.3.2(8) for relaxation, t is taken as 500,000 hours Concrete age coefficient (Expression (3.2)), βcc: βc c ( t ) = fc m ( t ) /fc m Expression (3.1) = exp{s[1-√(28/t)]} Expression (3.2) Coefficient for Class N cement, s = 0.25 βc c ( t 0 ) = exp{0.25[1.0-√(28/4.0)]} = 0.66269 βc c ( t ) = exp{0.25} = 1.28403 Characteristic strength of concrete, fc k = 40.0 MPa Mean compressive strength of concrete, fc m = 40.0 + 8.0 (from Table 3.1) = 48.0 MPa fc m 0 = 10.0 MPa fc m ( t 0 ) = βc c ( t 0 ) . fc m = 31.8094 MPa Ambient relative humidity = 80.0 % Notional size of member, h0 = 2Ac /u = 2*9.051E5/7245.89 = 249.811 mm Modulus of elasticity of concrete at 28 days, Ec m = 35.2205 GPa Modulus of elasticity of concrete at time considered, Ec m ( t ) = βc c ( t )

0.3

Expressions (3.5) & (3.1)

. Ec m

0.3

= 1.28403 * 35.2205 = 37.9636 GPa

Area of concrete cross section, Ac = 9.05E5 mm² Perimeter of concrete cross section, u = 7245.9 mm Notional size, h0 = 2*Ac /u = 2*9.051E5/7245.89 = 249.81 mm

Creep coefficient for concrete - EN 1992-1-1 clause 3.1.4 and Annex B.1 φ(t,t0 ) = φ0 . βc (t,t0 ) = φR H . β(fc m ) . β(t0 ) . βc (t,t0 )

SAM v6.50d

Expression (B.1) Expression (B.2)

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

123

Page: 5

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

for fc m >

35.0 MPa 1-RH/100 φR H = [ 1 + ——————————— . α1 ] .α2 0.33 0.1*h0 α1 = [35.0/48.0] α2 = [35.0/48.0] α3 = [35.0/48.0]

0.7 0.2 0.5

Expression (B.3b)

= 0.80163 = 0.93878 = 0.85391

φR H = [1.0 + (1.0-0.8) / (0.1*249.811 = 1.17777

0.33

) * 0.80163]*0.93878

β(fc m ) = 16.8/√fc m = 16.8/√48.0 = 2.42487

Expression (B.4)

For Permanent Loads

In the absence of heat curing t0 , T = 4.0 days age is adjusted for expression (B.5) (for cement type and temperature) - for cement class N (α = 0) 9.0

t0 = t0 , T . [ —————————————— + 1.0 ] 1.2 2.0 + t0 , T 9.0

= 4.0 =

α

* [ —————————————— + 1.0 ]

2.0 + 4.0 4.0 day

>=0.5

Expression (B.9)

0

1.2

0.2

β(t0 ) = 1/(0.1+t0 ) 0.2 = 1/(0.1+4.0 ) = 0.70446 βc (t,t0 ) = 1.0 for time t = ∞ hence from (B.1) and (B.2): φ(t,t0 ) = 1.17777*2.42487*0.70446 = 2.01193

Expression (B.5)

Check for creep non-linearity EN 1992-1-1 clause 3.1.4(4) At the level of the centroid of the tendons, the compressive stress in the concrete at time t0 = 0.0 MPa. This does not exceed 0.45*fck(t0), i.e. 18.0 MPa, so non-linear creep is not considered

Shrinkage Strain for concrete - EN 1992-1-1 clause 3.1.4(6) Total Shrinkage: εc s = εc d + εc a

SAM v6.50d

(3.8)

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

124

Page: 6

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Drying Shrinkage - Expression (3.9): εc d (t) = βd s (t,ts ).kh .εc d , 0 βd s (t,ts ) = 1.0 for t = ∞ From Table 3.3: kh = 0.80018 From Annex B, Expression (B.11):

-6

εc d , 0 = 0.85[(220+110.αd s 1 ).(exp(-αd s 2 .fc m /fc m 0 )].10 .βR H βR H = 1.55[1.0-(RH/100)³] (B.12) = 0.7564 For cement class N, αd s 1 = 4 αd s 2 = 0.12 hence, -6

εc d , 0 = 0.85[(220+110*4.0)*exp(-0.12*48.0/10.0)]*10 *0.7564 -6

and,

= 238.54*10

εc d (t) = 1.0*0.80018*238.54*10

-6

-6

= 190.877*10

Autogenous Shrinkage - Expression (3.11): εc a (t) = βa s (t).εc a (∞) βa s (t) = 1.0 for t = ∞ εc a (∞) = 2.5*(fc k -10.0)*10 -6 = 75.0*10 hence, εc a (t) = 1.0*75.0*10 = 75.0*10

-6

-6

-6

Total Shrinkage: εc s = εc d (t) + εc a (t) = 190.87688 + 75.0 = 265.87688*10

-6

Further Relaxation Clause 5.10.6(1)(b) Loss is calculated from clause 3.3.2(7) For tendon property Grade 1600 Ep 195.0 relaxation loss at 1000 hours, ρ1 0 0 0 = 8.0 % time after tensioning = 500000.0 hours μ = 0.75921 (as calculated for initial relaxation loss above) for Class 1 relaxation, use Expression (3.28) 6.7μ

5.39 . ρ1 0 0 0 . e

0.75(1-μ)

. [t/1000]

= 5.39 * 8.0 * 161.863 * 3.07185 * 10 = 0.21440

SAM v6.50d

-5

. 10

-5

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

125

Page: 7

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

With the initial relaxation deducted, the variation in tendon stress from relaxation becomes: Δσp r / σp i = 0.21440 - 0.04571 = 0.16868 Summary of the above for Expression (5.46):

Estimated shrinkage strain εc s Creep coefficient at t for loading at t0 φ(t,t0 ) Relaxation, Δσp r Modulus of elasticity for prestressing steel Ep Modulus of Elasticity for concrete Ec m Area of all prestressing Ap Area of concrete section Ac Second moment of area of concrete section Ic Ep /Ec m Ep /Ec m .Ap /Ac Ac /Ic

= 195.0/37.9636 = 5.1365*0.0/9.051E5 = 9.051E5/2.33E11

= = = = = = = =

265.877 2.01193 238.212 195.0 37.9636 0.0 9.051E5 2.33E11

= = =

5.1365 0.0 3.8904

-6

x10 MPa GPa GPa mm² mm² mm⁴

In the table below the following vary with tendon height: σc , Q P = Stress in concrete adjacent to tendons zc p = Section centre of gravity to tendons φ(t,t0 ) = Creep Coefficient (if non-linear creep is considered)  

 

height

 

 

mm

Ap mm²

shrink εc s .Ep MPa

relax 0.8Δσp r MPa

φ(t,t0 )

σc , Q P MPa

creep Ep /Ec m .φ.σ MPa

denom zc p mm

Total force loss: Total moment loss:

 

 

ΔPc + s + r kN 0.0 0.0

Mc s r = 0.0-(0.0*0.8997047) = 0.0 kN.m

Corresponding stresses - before composite: top stress = ( 0.0/5.372E5+0.0/1.284E8 )* 0.3 = ( 0.0+0.0 )* 0.3 = 0.0 MPa bottom stress = ( 0.0/5.372E5+0.0/-1.61E8 )* 0.3 = ( 0.0+0.0 )* 0.3 = 0.0 MPa top stress bottom stress

SAM v6.50d

= = = = = =

- after composite: ( 0.0/9.051E5+0.0/5.812E8 )*(1.0- 0.3) ( 0.0+0.0 )*(1.0-0.3) 0.0 MPa ( 0.0/9.051E5+0.0/-2.59E8 )*(1.0-0.3 ) ( 0.0+0.0 )*(1.0-0.3) 0.0 MPa

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

126

Page: 8

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Traffic gr1a TS - for Bending design 1 Loading

MA p p l i e d = 78.74031 kN.m PA p p l i e d = -19.96643 kN Corresponding stresses: top stress = -19.96643/905051.1 + 78.74031/5.8116E8 = -0.0221 + 0.13548 = 0.11342 MPa bottom stress = -19.96643/905051.1 + 78.74031/-2.586E8 = -0.0221 + -0.304 = -0.3265 MPa

Traffic gr1a UDL - for Bending design 1 Loading

MA p p l i e d = 32.7097 kN.m PA p p l i e d = -10.9063 kN Corresponding stresses: top stress = -10.9063/905051.1 + 32.7097/5.8116E8 = -0.0121 + 0.05628 = 0.04423 MPa bottom stress = -10.9063/905051.1 + 32.7097/-2.586E8 = -0.0121 + -0.126 = -0.1385 MPa

Traffic gr1a Footway - for Bending design 1 Loading

MA p p l i e d = 25.29156 kN.m PA p p l i e d = -3.118579 kN Corresponding stresses: top stress = -3.118579/905051.1 + 25.29156/5.8116E8 = -0.0034 + 0.04352 = 0.04007 MPa bottom stress = -3.118579/905051.1 + 25.29156/-2.586E8 = -0.0034 + -0.098 = -0.1012 MPa

TOTAL LOSS OF PRESTRESS SUMMARY Initial stressing force Prestress after all losses at t = ∞

= =

0.0 kN 0.0 kN

Corresponding loss = 100 %

LIMITING STRESSES IN PRECAST BEAM Compression EN 1992-2 Clause 7.2(102) k1 .fc k = 0.6*40.0 = 24.0 MPa In the presence of confinement or increase in cover this may be increased by up to 10%, i.e to: = 26.4 MPa

SAM v6.50d

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

127

Page: 9

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Tension Tension is governed by crack width considerations, and reinforcement provided for crack width control. Exposure Class is XD1, XD2, XD3, XS1, XS2, XS3 ... ... for which decompression is checked for the Frequent combination of loads. Decompression requires all of the tendon to be at least 65.0 mm above the level of the neutral axis.

LIMITING STRESSES FOR IN SITU CONCRETE Compression EN 1992-2-2 Clause 7.2(102) To avoid longitudinal cracking, compressive stress is limited to: σc = k1 .fc k = 0.6*31.875 = 19.125 MPa Tension Tension is governed by crack width considerations, and reinforcement provided for crack width control. EN 1992-1_1 Clause 7.3

TRANSMISSION LENGTH Bond stress at release, EN 1992-1-1 Clause 8.10.2.2(1) fb p t = ηp 1 .η1 .fc t d (t) where fc t d (t) = αc t .0.7fc t m (t)/γc fc t m (t) = -2.3253 MPa αc t = 1.0

[2]

- from EN 1992-1-1/3.1.6(2)

tendon type coefficient, bond condition coefficient, hence

Expression (8.15)

ηp 1 = η1 =

3.2 1.0

fc t d (t) = 1.0*0.7*-2.3253/1.5 = -1.0851 MPa

and

fb p t = 3.2*1.0*-1.0851 = -3.4724 MPa

SAM v6.50d

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

128

Page: 10

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Basic transmission length, EN 1992-1-1 Clause 8.10.2.2(2) lp t = α1 .α2 .φ.σp m 0 /fb p t where speed of release coefficient, tendon surface coefficient, nominal diameter of tendon, tendon stress after release,

hence

Expression (8.16)

α1 = α2 = φ = σp m 0 =

1.0 0.19 16.0 mm 1440.0 MPa

lp t = 1.0*0.19*16.0*1440.0 / 3.47242 = 1.26068 m

Design value of transmission length, EN 1992-1-1 Clause 8.10.2.2(3) lp t 1 = 0.8*lp t = 0.8*1.26068 = 1.00854 m

STRUCTURAL EFFECTS OF TIME DEPENDENT BEHAVIOUR EN 1992-2 Annex KK.7 Age of concrete at first loading, Age of concrete when first composite, Age of concrete at time considered, Creep coefficient when first composite, Final creep coefficient, Creep coefficient increment, Specified value of Ageing coefficient,

t0 = 4.0 days tc = 60.0 days t = ∞ φ(tc ,t0 ) = 0.89250 φ(∞,t0 ) = 2.00881 φ(∞,tc ) = 1.20422 χ = 0.8

From Expression (KK.119): φ(∞,t0 ) - φ(tc ,t0 ) 2.00881-0.89250 ————————————————— = ————————————————————— 1 + χ.φ(∞,tc ) 1.0 + 0.8*1.20422 = 0.56856

SAM v6.50d

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

129

Page: 11

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

SLS STRESS SUMMARY TABLE Concrete Stresses (MPa)

 

force kN

 

 

moment kN.m

In situ top bottom

Precast top bottom

CHARACTERISTIC PERMANENT ACTIONS AND PRESTRESS [3]

Prestress

0.0

Self Weight

0.0

0.0

0.0

0.0

0.0

0.0

—————————————————————————————————————————————————————— Prestress + Self Weight Elastic Def  

0.0

TRANSFER

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Erection

0.0

0.0

0.0

In situ 1A

0.0

0.0

0.0

Cr+Sh+Rlx

B

In situ 1B

0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

TOTAL PERMANENT EFFECTS, S0

 

Cr+Sh+Rlx

A

0.0

0.0

TOTAL PERMANENT EFFECTS, S0 , ∞

 

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

CREEP REDISTRIBUTION according to EN 1992-2 Annex KK.7 Construction On Centering, Sc = G + P1 + P2 Permanent G

0.0

0.0

0.0

0.0

0.0

Prestress P1

0.0

0.0

0.0

0.0

0.0

Prestress P2

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

(Sc - S0 )*0.56856 Hence from KK.119, TOTAL CONSTRUCTION EFFECTS, S∞

[4] [5]

 

 

SDL Diff. Shr. 1

605.383

0.0

0.0

0.0

0.0

0.0

286.182

-0.2604

-0.4932

1.16132

-0.4378

0.0

0.0

0.0

0.0

0.0

Diff. Shr. 2

[Differential shrinkage is included when adverse TOTAL PERMANENT EFFECTS [including diff. shrinkage

 

 

SAM v6.50d

0.0 -0.2604

0.0 -0.4932

] 0.0 1.16132

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

130

0.0 -0.4378]

Page: 12

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

VARIABLE ACTIONS - CHARACTERISTIC COMBINATION Traffic Selected case: Traffic gr1a TS

1

78.7403

0.18258

0.11855

0.13548

-0.3045

-0.0209

-0.0209

-0.0221

-0.0221

0.07585

0.04925

0.05628

-0.1265

-0.0114

-0.0114

-0.0121

-0.0121

0.05865

0.03808

0.04352

-0.0978

-0.0033

-0.0033

-0.0034

-0.0034

Total (Leading)

: 0.28154

0.17035

0.19773

-0.5663

Total (in Combination)

: 0.19177

0.11557

0.13427

-0.3893

-0.7655

-0.4970

-0.5680

1.27682

0.05356

0.05356

0.05663

0.05663

-0.3161

-0.2052

-0.2345

0.52720

0.02425

0.02425

0.02564

0.02564

0.05865

0.03808

0.04352

-0.0978

-0.0033

-0.0033

-0.0034

-0.0034

Total (Leading)

: -0.9484

-0.5896

-0.6803

1.78504

Total (in Combination)

: -0.7307

-0.4544

-0.5242

1.37422

-19.966 Traffic gr1a UDL 1

32.7097

-10.906 Traffic gr1a FT

1

25.2916

-3.1186

ψ0

0.75 0.75 0.4

Other traffic cases for comparison: Traffic gr1a TS

2

-330.15

51.2513 Traffic gr1a UDL 2

-136.32

23.2038 Traffic gr1a FT

2

25.2916

-3.1186

0.75 0.75 0.4

Temperature Restraint None defined Differential Temperature - Heating Diff. Tmp H1

-1016.0

Diff. Tmp H2

-413.84

2.47603

-0.8853

-0.8625

1.35841

0.0

0.0

0.0

0.0

0.0

143.384

-1.4373

0.52916

0.24758

-1.7606

2.0E-4

4.63E-7

3.01E-7

3.44E-7

-7.7E-7

0.6

Differential Temperature - Cooling Diff. Tmp C1

976.559

Diff. Tmp C2

0.6

Other Variable Action None defined The following combinations of variable actions are evaluated in accordance with EN 1990 Equation 6.14b: a) Traffic as leading action + ψ0(Thermal + Other) b) Thermal as leading action + ψ0(Traffic + Other) c) Other as leading action + ψ0(Traffic + Thermal) For thermal actions the following cases are considered: i) temperature restraint alone ii) differential temperature: Heating iii) differential temperature: Cooling iv) temperature restraint + differential temperature: Heating v) temperature restraint + differential temperature: Cooling

SAM v6.50d

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

131

Page: 13

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

The most adverse case is with Traffic as leading action

Traffic

0.28154

0.17035

0.19773

-0.5663

ψ0 x Thermal

1.48562

-0.5312

0.14855

-1.0564

0.0

0.0

0.0

0.0

ψ0 x Other  

 

TOTAL VARIABLE ACTIONS TOTAL PERMANENT (from above)

 

 

TOTAL COMBINATION

1.76716 -0.3608 0.34628 -1.6228 0.0 -0.4932 1.16132 -0.4378 —————————————————————————————————— 1.76716 -0.8540 1.50761 -2.0607

VARIABLE ACTIONS - FREQUENT COMBINATION Traffic Selected case:

ψ2

ψ1 = 0.75

Traffic gr1a TS

1

59.0552

-14.975 ψ1 = 0.75

Traffic gr1a UDL 1

24.5323

-8.1797 ψ1 =

0.13693

0.08891

0.10161

-0.2283

-0.0157

-0.0157

-0.0165

-0.0165

0.05688

0.03694

0.04221

-0.0949

-0.0085

-0.0085

-0.009

-0.009

0.0

0.0

0.4

however, EN 1991-2 Clause 4.5.2 excludes the footway loading from the frequent action of LM1 Traffic gr1a FT

1

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Total (Leading)

: 0.16962

Total (in Combination)

:

0.0

0.10164

0.11824

-0.3488

0.0

0.0

0.0

0.0

-0.5741

-0.3728

-0.4260

0.95761

0.04017

0.04017

0.04247

0.04247

-0.2370

-0.1539

-0.1759

0.39540

0.01819

0.01819

0.01923

0.01923

0.0

Other traffic cases for comparison: ψ1 = 0.75

Traffic gr1a TS

2

-247.61

38.4385 ψ1 = 0.75

Traffic gr1a UDL 2

-102.24

17.4029 ψ1 =

0.0

0.0

0.4

however, EN 1991-2 Clause 4.5.2 excludes the footway loading from the frequent action of LM1 Traffic gr1a FT

2

0.0 0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Total (Leading)

: -0.7528

-0.4683

-0.5402

1.41472

Total (in Combination)

:

0.0

0.0

0.0

0.0

0.0

Temperature Restraint None defined

SAM v6.50d

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

132

Page: 14

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Differential Temperature - Heating ψ1 =

0.6

Diff. Tmp H1

-1016.0

Diff. Tmp H2

-413.84

2.47603

-0.8853

-0.8625

1.35841

0.0

0.0

0.0

0.0

0.0

143.384

-1.4373

0.52916

0.24758

-1.7606

2.0E-4

4.63E-7

3.01E-7

3.44E-7

-7.7E-7

0.5

Differential Temperature - Cooling ψ1 =

0.6

Diff. Tmp C1

976.559

Diff. Tmp C2

0.5

Other Variable Action None defined The following combinations of variable actions are evaluated in accordance with EN 1990 Equation 6.15b: a) ψ1(Traffic) as leading action + ψ2(Thermal + Other) b) ψ1(Thermal) as leading action + ψ2(Traffic + Other) c) ψ1(Other) as leading action + ψ2(Traffic + Thermal) For thermal actions the following cases are considered: i) temperature restraint alone ii) differential temperature: Heating iii) differential temperature: Cooling iv) temperature restraint + differential temperature: Heating v) temperature restraint + differential temperature: Cooling The most adverse case is with Traffic as leading action

ψ1 x Traffic ψ2 x Thermal ψ2 x Other  

 

TOTAL VARIABLE ACTIONS TOTAL PERMANENT (from above)

 

 

TOTAL COMBINATION

0.16962

0.10164

0.11824

-0.3488

1.23801

-0.4426

0.12379

-0.8803

0.0

0.0

0.0

0.0

1.40764 -0.3410 0.24203 -1.2292 0.0 -0.4932 1.16132 -0.4378 —————————————————————————————————— 1.40764 -0.8342 1.40336 -1.6671

SLS FLEXURE Precast

 

Stress

 

(MPa)

 

After Transfer

After Erection

SAM v6.50d

T B

T B

E

Strain -6

Curvature -6

(x10 )

Deflection

(rad/m)

0.04918 ET 1.57982

2.16062

0.0

15.0561

-32.784

0.0

19.6107

-0.0383

Max.

-1.229

-0.2676 EI -14.415 0.52367

Here

(mm)

(x10 )

28.2042

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

133

Page: 15

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

After in situ 1A After in situ 1B

Long-term Dead

Diff. Temp H1 Diff. Temp H2 Diff. Temp C1 Diff. Temp C2

Traffic gr1a 1

T B T B

T B

T B T B T B T B

T B

-0.2562 EI -13.799 0.51456

1.1E-6 -2.5E-6

ES 3.12E-5

105.09

0.0

-4.8888

-29.104

0.0

1.59073

7.79E-5

0.0

-1.1726

26.3161

0.0

-1.4413

1.46E-5

0.0

0.40625

16.6888

0.0

-6.7548

92.6748

0.0

-12.688

-29.993 -1.3E-5

0.19773 ES 5.61411 -0.5663

5.84195

-7.0E-5

2.06E-7 ES 5.86E-6 -4.6E-7

0.0

23.1413

0.14855 ES 4.2178 -1.0564

-31.933

-37.408

-0.5175 ES -14.695 0.81504

6.14087

27.7139

1.16132 EL 99.2094 -0.4378

0.0

27.7139

-0.2562 EI -13.799 0.51456

-31.933

-16.081

Extreme in-service

Curvatures here are derived from precast section height: 1300.0mm ET = Elastic Modulus at Transfer = 31130.7MPa [EN1992-1-1 Clauses 3.1.3-(3) and 3.1.2-(6) with age 4 days] EI = Intermediate Term Elastic Modulus = 18567.1MPa [EN1992-1-1 Clause 7.4.3-(5) at 60.0 days (φ=0.89693)] EL = Long Term Elastic Modulus = 11705.8MPa [EN1992-1-1 Clause 7.4.3-(5) at infinite time (φ=2.00881)] ES = Short Term Elastic Modulus [Ecm]

= 35220.5MPa

________ [1] Refer to EN 1991-1-1 Table A.1 Note 1) [2] For the derivation of this value refer to the limiting stress calculations for transfer [3] includes draw-in and initial relaxation [4] With immediate losses and shrinkage / creep / relaxation losses until time at which insitu is cast. [5] Secondary effects arising from prestress in continuous section.

SAM v6.50d

06/02/2012 10:15:31

© 2012 Bestech Systems Ltd

134

Page: 16

Pre-tensioned Pre-stressed Beam Bridge Design Example

16.

Verification: ULS Shear - Pier

135

136

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design code: EN 1992-2:2005 with UK National Annex (modified) Analysis: Shears EN 1990 Equation 6.10 ULS Persistent / Transient Load case: Traffic gr1a TS - for Shear design 1 Section Ref 2 at 21m from left end of beam

WARNING - This analysis assumes that all tension steel (As) is adequately anchored to resist the required tensile forces. (Refer to clause 6.2.1(7), Figure 6.3, and clause 6.2.3(7) of EN1992-1-1).

Section details:

Ref 2 "Section 2" at 1 x span = 21 m from left end of beam

Analysis:

Traffic Actions: Shear for gr1a, loading I.D. 1 Ultimate Limit State: Persistent / Transient - EN 1990 Equation 6.10

SUMMARY OF ACTIONS PERMANENT ACTIONS  

ACTION TYPE

SHEAR kN

 

 

MOMENT kN.m

AXIAL kN

Beam erection before composite

= -190.3096

0.0

0.0

Construction stage 1A

= -101.1947

0.0

0.0

Construction stage 1B

= -36.56457

0.0

0.0

Surfacing

= -45.26953

-156.7871

0.0

Differential Shrinkage / creep

=

0.0

0.0

0.0

-373.3384

-156.7871

0.0

TOTAL PERMANENT ACTIONS,

SAM v6.50d

γG x Gk

06/02/2012 10:17:31

© 2012 Bestech Systems Ltd

137

[1]

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

VARIABLE ACTIONS  

ACTION TYPE

[2]

SHEAR kN

 

MOMENT AXIAL kN.m kN

ψ0

ψ1

ψ2

Traffic gr1a TS - for Shear design = -479.47 -407.05 37.0081 0.75 0.75

0.0

Traffic gr1a UDL - for Shear desig = -193.03 -710.42

0.0

Traffic gr1a Footway - for Shear d = -6.0115 TOTAL VARIABLE ACTIONS, γQ , 1 x Qk , 1 "+" Traffic leading:

Traffic

ψ0 x Other  

Other leading:

 

105.33 0.75 0.75

-46.95 -15.717

0.4

0.4

0.0

[3]

ΣγQ , i x ψ0 , i x Qk , i

-678.5098

-1164.427

126.62151

0.0

0.0

0.0

Total

-678.5098

-1164.427

126.62151

ψ0 x Traffic

-506.7783

-856.888

100.46704

Other

0.0

0.0

0.0

Total

-506.7783

-856.888

100.46704

-1051.848

-1321.214

126.62151

Critical case is with traffic leading

TOTAL COMBINATION  

This section is within a distance d from the face of a support. The following clauses therefore apply:

Clause 6.2.1(8)

The design shear reinforcement is taken as that which is required at the section a distance d from the face of the support. A check is carried out below that VEd does not exceed VRd,max.

Clause 6.2.2(6) and 6.2.3(8)

The load reduction factor β is not readily applicable to typical bridge loading, and it is conservative to ignore this clause.

SAM v6.50d

06/02/2012 10:17:31

© 2012 Bestech Systems Ltd

138

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Clause 6.2.3(103) and 6.2.3(4) Shear Resistance with design shear reinforcement characteristic strength of shear rft, fy w k = 500.0 MPa material partial factor γs = 1.15 design strength of shear rft fy w k /γs , fy w d = 434.783 MPa characteristic strength of concrete fc k = 40.0 MPa material partial factor γc = 1.5 design strength of concrete fc k /γc , fc d = 26.6667 MPa angle between compression strut & beam axis, θ = 35.0 ° cotθ = 1.42815 angle between shear rft and beam axis, α = π/2 rad axial force in cross section, NE d = 126.622 kN area of concrete cross section, Ac = 9.283E5 mm² concrete compressive stress NE d /Ac , σc p = 126.622/9.283E5 = 0.13640 MPa effective depth, d = 1407.5 mm distance from edge of support, a = 0.0 mm

Maximum Shear Force Value The maximum value of shear resistance is given by: VR d , m a x = αc w .bw .z.υ1 .fc d (cotθ + cotα)/(1 + cot²θ)

Expression (6.14)

compression chord stress coefficient, αc w : (Note 3) σc p /fc d = 0.13640 / 26.6667 = 0.00512 hence from Expression (6.11aN) αc w = 1.00512 minimum width between tension and compression chords, bw = 216.0 mm

[4]

inner lever arm, strength reduction factor, υ1 : υ = 0.6[1.0-fc k /250] = 0.6*(1.0-40.0/250.0) = 0.504 υ1 = υ(1-0.5cosα) = 0.504

z = 1231.81 mm

Expression (6.6N)

αc w .bw .z.υ1 .fc d = 1.00512*216.0*1231.81*0.504*26.6667 = 3594.3 kN since α = π/2, the expression (6.14) reduces to: VR d , m a x = αc w .bw .z.υ1 .fc d /(cotθ + tanθ) Expression (6.9) = 3594.3/(1.42815 + 0.70020) = 1680.17 kN which is greater than VE d - Vc c d - Vt d (1051.85 kN) and therefore OK.

SAM v6.50d

06/02/2012 10:17:31

© 2012 Bestech Systems Ltd

139

Page: 3

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Summary of link requirements along the beam:  

 

dimension from left beam end m

As w / s mm²/mm

MR d / ME d

[5]

Spacing in mm for link diameter [6]

10.0mm

 

0.0

0.21857

718.648

1.17

0.21857

718.648

1.35167

0.21857

718.648

1.51281

0.21857

718.648

2.0

0.21857

718.648

2.01204

0.21857

718.648

2.5

0.21857

718.648

2.86364

0.21857

718.648

3.51281

0.21857

718.648

4.01204

0.21857

718.648

4.51204

0.21857

718.648

4.77273

0.21857

718.648

6.68182

0.57756

8.59091

0.21857

1.7

271.969 718.648

10.5

0.21857

12.4091

0.59500

718.648

14.3182

0.21857

718.648

16.2273

0.21857

718.648

16.488

0.21857

718.648

16.9872

0.21857

718.648

17.4872

0.21857

718.648

18.0

0.21857

718.648

18.0

0.21857

718.648

18.1364

0.21857

718.648

1.69

263.998

18.5

0.21857

718.648

18.988

0.21857

718.648

19.0

0.21857

19.4872

1.30135

17.9

718.648 120.705

19.5925

1.31204

11.9

119.722

20.0454

1.31204

11.9

119.722

21.0

1.31204

11.9

119.722

The interface shear requirement may be critical. Warning: At the locations indicated in the table above, additional longitudinal reinforcement is required to carry the shear in the tension chord of the truss.

SAM v6.50d

06/02/2012 10:17:31

© 2012 Bestech Systems Ltd

140

Page: 4

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

location.

The reinforcement requirements are calculated in the results for the relevant design

________ [1] Shrinkage effects are excluded at ULS in accordance with EN1992-1-1/2.3.2.2(2) [2] Thermal effects are not considered for ULS Shear in accordance with EN 1992-1-1 clause 2.3.1.2(2) [3] EN 1991-2 Clause 4.5.2 excludes the footway loading from the frequent action of LM1 [4] The inner lever arm is derived by analysing the section for the resistance moment and dividing the moment by the reinforcement tension force. (Using the resistance moment gives a conservative result). [5] The reduced resistance moment MRd is calculated for locations where design shear reinforcement is required. MRd/MEd must be greater than 1.0. [6] Based on 2 legs (double this value if using 4 legs)

SAM v6.50d

06/02/2012 10:17:31

© 2012 Bestech Systems Ltd

141

Page: 5

142

Pre-tensioned Pre-stressed Beam Bridge Design Example

17.

Verification: ULS Interface Shear

143

144

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design code: EN 1992-2:2005 with UK National Annex (modified) Analysis: Longitudinal Shear EN 1990 Equation 6.10 ULS Persistent / Transient Load case: Traffic gr1a TS - for Shear design 1 Section Ref 2 at 21m from left end of beam

Section details:

Ref 2 "Section 2" at 1 x span = 21 m from left end of beam

Analysis:

Interface and web/flange shear for gr1a, loading I.D. 1 Ultimate Limit State: Persistent / Transient - EN 1990 Equation 6.10

SUMMARY OF ACTIONS PERMANENT ACTIONS  

ACTION TYPE

SHEAR kN

 

 

Beam erection before composite

= -190.3096

Construction stage 1A

= -101.1947

Construction stage 1B

= -36.56457

Surfacing

= -45.26953

Differential Shrinkage / creep

=

TOTAL PERMANENT ACTIONS,

SAM v6.50d

γG x Gk

0.0

[1]

-373.3384

06/02/2012 09:29:02

© 2012 Bestech Systems Ltd

145

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

VARIABLE ACTIONS [2]

 

ACTION TYPE

SHEAR kN

 

Traffic gr1a TS - for Shear design =

ψ0

ψ1

ψ2

-479.468

0.75 0.75

0.0

Traffic gr1a UDL - for Shear desig = -193.0303

0.75 0.75

0.0

Traffic gr1a Footway - for Shear d = -6.011462 TOTAL VARIABLE ACTIONS, γQ , 1 x Qk , 1 "+" Traffic leading:

Traffic

Other leading:

 

0.4

[3]

0.0

ΣγQ , i x ψ0 x Qk , i

-678.5098

ψ0 x Other  

0.4

0.0

Total

-678.5098

ψ0 x Traffic

-506.7783

Other

0.0

Total

-506.7783

Critical case is with traffic leading

TOTAL COMBINATION  

-1051.848

Clause 6.2.5 INTERFACE SHEAR CALCULATIONS This section is within a distance d from the face of a support. The following clause therefore applies:

Clause 6.2.1(8)

The design shear is taken as that which is present at the section which is a distance d from the face of the support.

SAM v6.50d

06/02/2012 09:29:02

© 2012 Bestech Systems Ltd

146

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Summary of link requirements along the beam:  

 

 

dimension from left beam end m

Flexural Shear As w / s mm²/mm

Interface Shear As w / s 6.2.5(3) mm²/mm

suggestion

Spacing in mm for link diameter [4]

10.0mm

0.0

0.21857

2.5653

2.33209

67.3557

1.17

0.21857

2.5653

2.33209

67.3557

1.35167

0.21857

2.5653

2.33209

67.3557

1.51281

0.21857

2.54248

2.33209

67.3557

2.0

0.21857

2.47351

2.33209

67.3557

2.01204

0.21857

2.47181

2.33209

67.3557

2.5

0.21857

2.40275

2.33209

67.3557

2.86364

0.21857

2.3513

2.33209

67.3557

3.51281

0.21857

2.17865

2.33209

67.3557

4.01204

0.21857

2.04589

1.98059

79.3095

4.51204

0.21857

1.91325

1.98059

79.3095

4.77273

0.21857

1.84411

1.98059

79.3095

6.68182

0.57756

1.37475

1.67646

93.697

8.59091

0.21857

0.70216

1.24977

125.687

10.5

0.21857

0.96417

1.2875

122.003

12.4091

0.59500

1.41625

1.68008

93.4954

14.3182

0.21857

1.84809

2.07448

75.7201

16.2273

0.21857

2.28193

2.36788

66.3377

16.488

0.21857

2.34875

2.36788

66.3377

16.9872

0.21857

2.47674

2.36788

66.3377

17.4872

0.21857

2.60467

2.83907

55.3279

18.0

0.21857

2.73586

2.83907

55.3279

18.0

0.21857

2.73586

2.83907

55.3279

18.1364

0.21857

2.77085

2.83907

55.3279

18.5

0.21857

2.85884

2.83907

55.3279

18.988

0.21857

2.97693

2.83907

55.3279

19.0

0.21857

2.97984

2.83907

55.3279

19.4872

1.30135

3.09753

2.83907

55.3279

19.5925

1.31204

3.12298

2.83907

55.3279

20.0454

1.31204

3.12298

2.83907

55.3279

21.0

1.31204

3.12298

2.83907

55.3279

________ [1] Shrinkage effects are excluded at ULS in accordance with EN1992-1-1/2.3.2.2(2) [2] Thermal effects are not considered for ULS Shear in accordance with EN 1992-1-1 clause 2.3.1.2(2) [3] EN 1991-2 Clause 4.5.2 excludes the footway loading from the frequent action of LM1 [4] Based on 2 legs (double this value if using 4 legs)

SAM v6.50d

06/02/2012 09:29:02

© 2012 Bestech Systems Ltd

147

Page: 3

148

Pre-tensioned Pre-stressed Beam Bridge Design Example

18.

Verification: Web Shear Cracking

149

150

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Design code: Analysis:

EN 1992-2:2005 with UK National Annex (modified) Shears at time t=infinity EN 1990 Equation 6.15 SLS Frequent Exposure Class: XD1, XD2, XS1, XS2, XS3 Load case: Traffic gr1a TS - for Shear design 1 Section Ref 2 at 21m from left end of beam

WARNING - This analysis assumes that all tension steel (As) is adequately anchored to resist the required tensile forces. (Refer to clause 6.2.1(7), Figure 6.3, and clause 6.2.3(7) of EN1992-1-1).

Section details:

Ref 2 "Section 2" at 1 x span = 21 m from left end of beam

Analysis:

Traffic Actions: Shear for gr1a, loading I.D. 1 At time considered, t = ∞ Serviceability Limit State: Frequent - EN 1990 Equation 6.15

SUMMARY OF ACTIONS

SAM v6.50d

06/02/2012 16:36:18

© 2012 Bestech Systems Ltd

151

Page: 1

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

PERMANENT ACTIONS  

ACTION TYPE

SHEAR kN

 

AXIAL kN

Beam erection before composite

=

-140.97

0.0

0.0

Construction stage 1A

= -74.95901

0.0

0.0

Construction stage 1B

= -27.08487

0.0

0.0

Surfacing

= -37.72461

-130.6559

0.0

=

9.715637

-203.8871

0.0

-271.0229

-334.543

0.0

Differential Shrinkage / creep  

MOMENT kN.m

TOTAL PERMANENT ACTIONS,

Gk

VARIABLE ACTIONS  

ACTION TYPE

SHEAR kN

 

MOMENT kN.m

AXIAL kN

ψ0

ψ1

ψ2

Traffic gr1a TS - for Shear design = -355.16 -301.52 27.4134 0.75 0.75

0.0

Traffic gr1a UDL - for Shear desig = -142.99 -526.24 78.0224 0.75 0.75

0.0

Traffic gr1a Footway - for Shear d = -4.4529 -34.778 -11.642

0.0

TOTAL VARIABLE ACTIONS, ψ1 , 1 x Qk , 1 "+" Traffic leading:

Other leading:

 

0.4

ψ1 x Traffic

-373.6102

-620.8208

79.076887

0.0

0.0

0.0

Total

ψ2 x Other  

Σψ2 , i x Qk , i

0.4

-373.6102

-620.8208

79.076887

ψ2 x Traffic

0.0

0.0

0.0

ψ1 x Other

0.0

0.0

0.0

Total

0.0

0.0

0.0

-644.633

-955.3638

79.076887

[1]

Critical case is with traffic leading

TOTAL COMBINATION  

SAM v6.50d

06/02/2012 16:36:18

© 2012 Bestech Systems Ltd

152

Page: 2

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

WEB SHEAR CRACKING EN 1992-2 Annex QQ Characteristic strength of concrete in web, fc k Characteristic tensile strength 5% fractile, fc t k ; 0 , 0 5 Design shear on precast section before composite, VE d , 1 Total design shear on precast section, VE d Design shear on precast section after composite, VE d , 2 Stress in precast from Prestress P and bending ME d : at the top of the precast section, at the bottom of the precast section,

= = = = =

40.0 MPa -2.4562 MPa 243.01388 kN 654.34866 kN 411.33479 kN

σa = -1.1362 MPa σb = 3.32705 MPa

Height of precast section,

h =

1300.0 mm

Principal tensile stress is checked at the level of the centroid, and in addition at 100 points through the depth of the section to find the critical level.

First check at the composite section centroid: At the composite section centroid,

zf , m a x = 912.41288 mm

At this height: width of precast section, b = 354.58722 mm direct stress, σc 1 = σb + zf , m a x /h*(σa -σb ) = 3.32705 + 912.413/1300.0*(-1.1362-3.32705) = 0.19452 MPa For precast section: area beyond level zf , m a x first moment of area second moment of area

A1 = 1.547E5 mm² (A.z)1 = 8.269E7 mm³ Iy y , 1 = 9.2977E10 mm⁴

Shear stress at height zf , m a x τy z , E d , 1 = VE d , 1 * (A.z)1 /(Iy y , 1 .b) = 243.014 * 8.269E7 / (9.2977E10*354.587) = 0.60953 MPa For composite section: area beyond level zf , m a x (transformed) A2 = 3.825E5 mm² first moment of area (A.z)2 = 2.113E8 mm³ second moment of area Iy y , 2 = 2.3848E11 mm⁴

SAM v6.50d

06/02/2012 16:36:18

© 2012 Bestech Systems Ltd

153

Page: 3

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Shear stress at level zf , m a x τy z , E d , 2 = VE d , 2 * (A.z)2 /(Iy y , 2 .b) = 411.335 * 2.113E8 / (2.3848E11*354.587) = 1.02807 MPa total shear stress,

τy z , E d = 0.60953 + 1.02807 = 1.63761

From Mohr's circle: centre, σc 0 = 0.5*(0.19452+0.0) radius,

σr

=

√[τy z , E d

2

= 0.09726 MPa

2

+ (σc 1 -σc 0 ) ]

= 1.64049 MPa

σ3 = 0.09726 + 1.64049 = 1.73776 MPa σ1 = 0.09726 - 1.64049 = -1.5432 MPa From Expression QQ.101, and using Annex QQ sign convention, σ1 = 1.54323 MPa fc t b = [1 - 0,8.(σ3 /fc k )].fc t k ; 0 , 0 5 = 0.96524 * 2.45617 = 2.37081 MPa

Now checking through the depth of the section:

Level at which critical tension stress occurs, zf , m a x = 442.0 mm At this height: width of precast section, b = 218.2 mm direct stress, σc 1 = σb + zf , m a x /h*(σa -σb ) = 3.32705 + 442.0/1300.0*(-1.1362-3.32705) = 1.80956 MPa For precast section: area beyond level zf , m a x first moment of area second moment of area

[2]

A1 = 2.489E5 mm² (A.z)1 = 9.905E7 mm³ Iy y , 1 = 9.2977E10 mm⁴

Shear stress at height zf , m a x τy z , E d , 1 = VE d , 1 * (A.z)1 /(Iy y , 1 .b) = 243.014 * 9.905E7 / (9.2977E10*218.2) = 1.18646 MPa For composite section: area beyond level zf , m a x (transformed) A2 = 2.489E5 mm² first moment of area (A.z)2 = 1.828E8 mm³ second moment of area Iy y , 2 = 2.3848E11 mm⁴

SAM v6.50d

06/02/2012 16:36:18

© 2012 Bestech Systems Ltd

154

Page: 4

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

Shear stress at level zf , m a x τy z , E d , 2 = VE d , 2 * (A.z)2 /(Iy y , 2 .b) = 411.335 * 1.828E8 / (2.3848E11*218.2) = 1.44478 MPa total shear stress,

τy z , E d = 1.18646 + 1.44478 = 2.63124

From Mohr's circle: centre, σc 0 = 0.5*(1.80956+0.0) radius,

σr

=

√[τy z , E d

2

= 0.90478 MPa

2

+ (σc 1 -σc 0 ) ]

= 2.78246 MPa

σ3 = 0.90478 + 2.78246 = 3.68724 MPa σ1 = 0.90478 - 2.78246 = -1.8777 MPa From Expression QQ.101, and using Annex QQ sign convention, σ1 = 1.87767 MPa fc t b = [1 - 0,8.(σ3 /fc k )].fc t k ; 0 , 0 5 = 0.92625 * 2.45617 = 2.27505 MPa which is greater than σ1, so minimum reinforcement in accordance with 7.3.2 should be provided. ________ [1] EN 1991-2 Clause 4.5.2 excludes the footway loading from the frequent action of LM1 [2] Nearest multiple of depth/100

SAM v6.50d

06/02/2012 16:36:18

© 2012 Bestech Systems Ltd

155

Page: 5

156

Pre-tensioned Pre-stressed Beam Bridge Design Example

Appendix - National Annex NDP Values

157

158

Bestech Systems Limited 2 Slaters Court Princess Street Knutsford WA16 6BW Job:

Sample Reports

Beam:

Prestress Beam - Inner span 1 Eurocode + UK NA

Job No.:   6.5d Calc. By:   dlg Checked:   

Data File: J:\...\6.50d Data Files\inner beam span 1.sam 02/02/2012 09:39:44

NATIONALLY DETERMINED PARAMETERS European Standard EN1990 Description

Current

United Kingdom NDPs

Category A: domestic; residential area

0.7

0.7

Category B: office areas

0.7

0.7

Category C: congregation areas

0.7

0.7

Category D: shopping areas

0.7

0.7

Category E: storage areas

1

1

Category F: traffic area; vehicle weight