Sam Eurocode UK Pretressed Beam Sample Report

Full text

(1)Sample Report Precast Pre-tensioned Beam Example Eurocodes UK NA.

(2)

(3) 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) 4.

(5) Pre-tensioned Pre-stressed Beam Bridge Design Example. 1. Geometry & Basic Data. 5.

(6) 6.

(7) 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.

(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. . 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.

(9) Pre-tensioned Pre-stressed Beam Bridge Design Example. 2. Carriageway Configuration. 9.

(10) 10.

(11) 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.

(12) 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.

(13) Pre-tensioned Pre-stressed Beam Bridge Design Example 3. Global Analysis Model. 13.

(14) 14.

(15) 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) 16.

(17) 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) 18.

(19) 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.

(20) 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.

(21) 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) 22.

(23) 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) 24.

(25) 25.

(26) 26.

(27) 27.

(28) 28.

(29) 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) 30.

(31) 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. <Filter is Empty> 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) 32.

(33) 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. <Filter is Empty>. SAM v6.50d Copyright © 2012 Bestech Systems Ltd. 02/02/2012 11:31. 33. 1.

(34) 34.

(35) 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. <Filter is Empty> 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) 36.

(37) Pre-tensioned Pre-stressed Beam Bridge Design Example. 7. Section Properties a) Mid Span b) Internal Support. 37.

(38) 38.

(39) 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.

(40) 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.

(41) 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.

(42) 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.

(43) Pre-tensioned Pre-stressed Beam Bridge Design Example. 8. Data Summary after Tendon Design. 43.

(44) 44.

(45) 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.

(46) 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.

(47) 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.

(48) 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.

(49) 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.

(50) 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.

(51) Pre-tensioned Pre-stressed Beam Bridge Design Example. 9. Temperature Gradient. 51.

(52) 52.

(53) 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.

(54) 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.

(55) Pre-tensioned Pre-stressed Beam Bridge Design Example 10.. 55. Shrinkage & Creep.

(56) 56.

(57) 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.

(58) 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.

(59) 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.

(60) 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.

(61) 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.

(62) 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.

(63) Pre-tensioned Pre-stressed Beam Bridge Design Example. 11.. Verification: Transfer Stresses. 63.

(64) 64.

(65) 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.

(66) 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.

(67) 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.

(68) 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.

(69) 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 <= 0.6*fc k (t) Equation 5.42 = 0.6 * 23.8094 = 14.2857 MPa hence limiting compression stress = 14.285666 MPa This may be increased if justified to: σc <= k6 .fc k (t) = 0.7 * 23.8094 = 16.6666 MPa Tension Tension is governed by crack width considerations, and reinforcement provided for crack width control. EN 1992-1-1 Clause 7.3.2(4) No reinforcement is required for tensile stress less than σct,p where: σc t , p = fc t , e f f from clause 7.3.2(2), fc t , e f f = fc t m (t) (2/3). fc t m = 0.3*fc k (from Table 3.1) = -3.5088 MPa fc t m (t) = βc c (t).fc t m (clause 3.1.2(9)) = 0.66269*-3.5088 = -2.3253 MPa hence limiting tension stress = -2.325284 MPa [Note: at transfer, the characteristic combination of loads is the same as the frequent combination of loads, and this stress limit might therefore be considered to be higher than appropriate]. SAM v6.50d. 15/02/2012 15:36:54. © 2012 Bestech Systems Ltd. 69. Page: 5.

(70) 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. 15/02/2012 15:36:54. © 2012 Bestech Systems Ltd. 70. Page: 6.

(71) 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. 769.979. 5.9954. -4.7704. —————————————————————————————————————————————————————— Prestress + Self Weight. . 1.84555. 12.7201. Elastic Def. -201.86. 89.2851. 0.31947. -0.9289. TRANSFER. 4043.05. -688.47. 2.16502. 11.7912. SLS FLEXURE Precast. . Stress. . (MPa). . After Transfer. T B. E. Strain -6. Curvature -6. (x10 ). Deflection (mm). (x10 ). (rad/m). Here. 2.16502 ET 69.5462. -237.86. 14.6578. 11.7912. Max.. 14.6578. 378.765. 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]. ________ [1] Refer to EN 1991-1-1 Table A.1 Notes 1) and 2) [2] For the derivation of this value refer to the limiting stress calculations for transfer [3] includes draw-in and initial relaxation. SAM v6.50d. 15/02/2012 15:36:54. © 2012 Bestech Systems Ltd. 71. Page: 7.

(72) 72.

(73) Steel Composite Bridge Design Example. 12.. Verification: SLS Bending - Mid Span. 73.

(74) 74.

(75) 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 10.5m 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 0.5 x span = 10.5 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. 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. 06/02/2012 10:09:59. © 2012 Bestech Systems Ltd. 75. Page: 1.

(76) 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. 06/02/2012 10:09:59. © 2012 Bestech Systems Ltd. 76. Page: 2.

(77) 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 = 25.0 kN/m³ self weight = 5.372E5*25.0 = 13.4306 kN/m beam length = 21.0 m distance = 10.5 m Ms w = 0.5*13.4306*10.5*(21.0-10.5) = 740.364 kN.m Corresponding stresses: top stress = 740.364/1.2843E8 = 5.76481 MPa bottom stress = 740.364/-1.614E8 = -4.5869 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. = 1.61496 MPa = 12.9036 MPa = 1300.0 mm = 31.1307 GPa. 06/02/2012 10:09:59. © 2012 Bestech Systems Ltd. 77. Page: 3.

(78) 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. 12.38261. 3.978E-4. 127.97976. 7.6787854. 110.0. 4. 11.94843. 3.838E-4. 44.906297. 4.9396927. 210.0. 2. 11.08007. 3.559E-4. 20.821353. 4.3724841. 260.0. 2. 10.64589. 3.42E-4. 20.005455. 5.2014182. 1200.0. 2. 2.483314. 7.977E-5. 4.6665732. 5.5998878. 218.37943. 27.792268. TOTAL. 21. Moment about the centroid of the precast beam: Me d = 27.792268-(218.37943*0.5760392) = -98.00285 kN.m hence, top stress = 1.615-218.37943/537.22568--98.00285/1.2843E8 = 1.615-0.4064947--0.763094 = 1.9715546 MPa bottom stress = 12.904-218.37943/537.22568--98.00285/-1.614E8 = 12.904-0.4064947-0.6071768 = 11.889955 MPa After a further 2 iterations of the above process, the top and bottom stresses are as follows: top stress = 1.94149211 MPa bottom stress = 11.9620665 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 = 1330.61 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 = 738.00575 kN.m Corresponding stresses: top stress = 738.00575/1.2843E8 = 5.74644 MPa bottom stress = 738.00575/-1.614E8 = -4.5723 MPa Remove the dead load applied for transfer calculations Ms w = -740.36 kN.m. SAM v6.50d. 06/02/2012 10:09:59. © 2012 Bestech Systems Ltd. 78. Page: 4.

(79) 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. Corresponding stresses: top stress = -740.36/1.2843E8 = -5.7648 MPa bottom stress = -740.36/-1.614E8 = 4.58693 MPa. Construction stage 1A Loading. MA p p l i e d = 512.3149 kN.m Corresponding stresses: top stress = 512.3149/1.2843E8 = 3.98911 MPa bottom stress = 512.3149/-1.614E8 = -3.174 MPa. Construction stage 1B Loading. MA p p l i e d = 21.87451 kN.m Corresponding stresses: top stress = 21.87451/1.2843E8 = 0.17032 MPa bottom stress = 21.87451/-1.614E8 = -0.1355 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 28.63 % 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) adjusted t0 = t0 , T . [(9/(2+t0 , T = 4.0 * [(9/(2+4.0 = 4.0 days. SAM v6.50d. 1.2. 1.2. )+1). )+1]. 0. α. >=0.5. 06/02/2012 10:09:59. © 2012 Bestech Systems Ltd. 79. Expression (B.9). Page: 5.

(80) 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 = ∞ 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, 0.3. Ec m ( t ) = βc c ( t ) . Ec m 0.3 = 1.28403 * 35.2205 = 37.9636 GPa. Expressions (3.5) & (3.1). 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 ). Expression (B.1) Expression (B.2). 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. 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.

(81) 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.

No results found