Stress at Ultimate in Prestressed Unbonded Tendons: Assessment of Code Equations and Recommendation

1. ACI Committee 318, 2019, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19),” American Concrete Institute, Farmington Hills, MI, 624 pp.

2. Alkhairi, F. M., and Naaman, A. E., 1993, “Analysis of Beams Prestressed with Unbonded Internal or External Tendons,” Journal of Structural Engineering, ASCE, V. 119, No. 9, pp. 2680-2700. doi: 10.1061/(ASCE)0733-9445(1993)119:9(2680)10.1061/(ASCE)0733-9445(1993)119:9(2680) ↗

3. Allouche, E. N.; Campbell, T. I.; Green, M. F.; and Soudki, K. A., 1999, “Tendon Stress in Continuous Unbonded Prestressed Concrete Members Part 2: Parametric Study,” PCI Journal, V. 44, No. 1, pp. 60-73. doi: 10.15554/pcij.01011999.60.7310.15554/pcij.01011999.60.73 ↗

4. Alqam, M., and Alkhairi, F. M., 2019, “Numerical and Analytical Behavior of Beams Prestressed with Unbonded Internal or External Steel Tendons: A State-of-the-Art Review,” Arabian Journal for Science and Engineering, V. 44, No. 10, pp. 8149-8170. doi: 10.1007/s13369-019-03934-310.1007/s13369-019-03934-3 ↗

5. Alqam, M.; Alkhairi, F. M.; and Naaman, A. E., 2020, “An Improved Methodology for the Prediction of the Stress at Ultimate in Unbonded Internal and External Steel Tendons,” Arabian Journal for Science and Engineering, V. 45, No. 10, pp. 7915-7954. doi: 10.1007/s13369-020-04475-w10.1007/s13369-020-04475-w ↗

6. American Association of State Highway and Transportation Officials, 1994, “LRFD Bridge Design Specifications,” first edition, AASHTO, Washington, DC.

7. American Association of State Highway and Transportation Officials, 2017, “LRFD Bridge Design Specifications,” eighth edition, AASHTO, Washington, DC, 1781 pp.

8. Aparicio, A. C.; Ramos, G.; and Casas, J. R., 2002, “Testing of Externally Prestressed Concrete Beams,” Engineering Structures, V. 24, No. 1, pp. 73-84. doi: 10.1016/S0141-0296(01)00062-110.1016/S0141-0296(01)00062-1 ↗

9. Au, F. T. K.; Su, R. K. L.; Tso, K.; and Chan, K. H. E., 2008, “Behaviour of Partially Prestressed Beams with External Tendons,” Magazine of Concrete Research, V. 60, No. 6, pp. 455-467. doi: 10.1680/macr.2008.60.6.45510.1680/macr.2008.60.6.455 ↗

10. Canadian Standards Association, 2014, “Design of Concrete Structures (CSA A23.3-14),” CSA, Mississauga, ON, Canada.

11. Chakrabarti, P. R., 1995, “Ultimate Partially Stress for Unbonded Post-Tensioning Tendons in Prestressed Beams,” ACI Structural Journal, V. 92, No. 6, Nov.-Dec,. pp. 689-697.10.14359/9663 ↗

12. Chakrabarti, P. R., and Whang, T. P., 1989, “Study of Partially Prestressed Beams with Unbonded Post-Tensioning,” Proceedings, American Society of Civil Engineers, Reston, VA, pp. 189-200.

13. China Academy of Building Research, 2004, “Technical Specification for Concrete Structures Prestressed with Unbonded Tendons (JGJ 92-2004),” CABR, Beijing, China.

14. Chouinard, K. L., 1989, “Tendon Stress at Ultimate in Unbonded Partially Prestressed Concrete Beams,” Msc thesis, Department of Civil Engineering, Queen’s University, Kingston, ON, Canada.

15. Cooke, N.; Park, R.; and Yong, P., 1981, “Flexural Strength of Prestressed Concrete Members with Unbonded Tendons,” PCI Journal, V. 26, No. 6, pp. 52-90. doi: 10.15554/pcij.11011981.52.8110.15554/pcij.11011981.52.81 ↗

16. Deutsches Institut fur Normung, 2001, “Concrete, Reinforced and Prestressed Concrete Structures—Part 1: Design and Construction (DIN 1045-1:2001),” DIN, Berlin, Germany.

17. Du, G., and Tao, X., 1985, “Ultimate Stress of Unbounded Tendons in Partially Prestressed Concrete Beams,” PCI Journal, V. 30, No. 6, pp. 72-91. doi: 10.15554/pcij.11011985.72.9110.15554/pcij.11011985.72.91 ↗

18. Du, J. S., 2007, “Experimental Study of Partially Prestressed Concrete Beams with External CFRP Tendons (Research Report),” School of Civil Engineering, Beijing Jiao Tong University, Beijing, China. (in Chinese)

19. Ghallab, A., and Beeby, A. W., 2005, “Factors Affecting the External Prestressing Stress in Externally Strengthened Prestressed Concrete Beams,” Cement and Concrete Composites, V. 27, No. 9-10, pp. 945-957. doi: 10.1016/j.cemconcomp.2005.05.00310.1016/j.cemconcomp.2005.05.003 ↗

20. Harajli, M., and Kanj, M., 1991, “Ultimate Flexural Strength of Concrete Members Prestressed with Unbonded Tendons,” ACI Structural Journal, V. 88, No. 6, Nov.-Dec., pp. 663-673.10.14359/1258 ↗

21. Harajli, M. H., and Hijazi, S. A., 1991, “Evaluation of the Ultimate Steel Stress in Partially Prestressed Concrete Members,” PCI Journal, V. 36, No. 1, pp. 62-82. doi: 10.15554/pcij.01011991.62.8210.15554/pcij.01011991.62.82 ↗

22. Heo, S.; Shin, S.; and Lee, C., 2013, “Flexural Behavior of Concrete Beams Internally Prestressed with Unbonded Carbon-Fiber-Reinforced Polymer Tendons,” Journal of Composites for Construction, ASCE, V. 17, No. 2, pp. 167-175. doi: 10.1061/(ASCE)CC.1943-5614.000030610.1061/(ASCE)CC.1943-5614.0000306 ↗

23. Khairallah, N., and Harajli, M. H., 1997, “Experimental and Analytical Evaluation of the Behavior of Concrete T Beams with External Prestressing (Research Report),” Department of Civil and Environmental Engineering, Faculty of Engineering and Architecture, American University of Beirut, Beirut, Lebanon.

24. Kim, Y. J., 2010, “Flexural Response of Concrete Beams Prestressed with AFRP Tendons: Numerical Investigation,” Journal of Composites for Construction, ASCE, V. 14, No. 6, pp. 647-658. doi: 10.1061/(ASCE)CC.1943-5614.000012810.1061/(ASCE)CC.1943-5614.0000128 ↗

25. Le, T. D.; Pham, T. M.; Hao, H.; and Hao, Y., 2018, “Flexural Behaviour of Precast Segmental Concrete Beams Internally Prestressed with Unbonded CFRP Tendons under Four-Point Loading,” Engineering Structures, V. 168, Aug, pp. 371-383. doi: 10.1016/j.engstruct.2018.04.06810.1016/j.engstruct.2018.04.068 ↗

26. Mattock, A. H.; Yamazaki, J.; and Kattula, B. T., 1971, “Comparative Study of Prestressed Concrete Beams, with and without Bond,” ACI Journal Proceedings, V. 68, No. 2, Feb., pp. 116-125.10.14359/11298 ↗

27. Mojtahedi, S., and Gamble, W., 1978, “Ultimate Steel Stresses in Unbonded Prestressed Concrete,” Journal of the Structural Division, V. 104, No. 7, pp. 1159-1165. doi: 10.1061/JSDEAG.000495710.1061/JSDEAG.0004957 ↗

28. Naaman, A. E., 1990, “New Methodology for the Analysis of Beams Prestressed with External or Unbonded Tendons,” External Prestressing in Bridges, SP-120, June pp. 339-354.

29. Naaman, A. E., 1991, “Stress at Ultimate in Unbonded Prestressing Tendons by Strain Compatibility,” Progress in Structural Engineering, Solid Mechanics and Its Applications, D. E. Grierson, A. Franchi, and P. Riva, eds., Springer, Dordrecht, the Netherlands, pp. 217-227.10.1007/978-94-011-3616-7_15 ↗

30. Naaman, A. E., 2005, “PC Beams with Unbonded Tendons: Analysis in Cracked, Uncracked and Ultimate State,” Ned H. Burns Symposium on Historic Innovations in Prestressed Concrete, SP-231, Oct., pp. 105-127.

31. Naaman, A. E., 2012, Prestressed Concrete Analysis and Design: Fundamentals, third edition, Techno Press 3000, Ann Arbor, MI, 1176 pp.

32. Naaman, A. E., and Alkhairi, F. M., 1991a, “Stress at Ultimate in Unbonded Post-Tensioning Tendons: Part 1—Evaluation of the State of the Art,” ACI Structural Journal, V. 88, No. 5, Sept.-Oct., pp. 641-651.10.14359/2763 ↗

33. Naaman, A. E., and Alkhairi, F. M., 1991b, “Stress at Ultimate in Unbonded Post-Tensioning Tendons: Part 2—Proposed Methodology,” ACI Structural Journal, V. 88, No. 6, Nov.-Dec., pp. 683-692.10.14359/1288 ↗

34. Naaman, A. E.; Burns, N.; French, C.; Gamble, W. L.; and Mattock, A. H., 2002, “Stresses in Unbonded Prestressing Tendons at Ultimate: Recommendation,” ACI Structural Journal, V. 99, No. 4, July-Aug., pp. 518-529. See also discussion and closure in V. 100, No. 3, May-June 2003, pp. 394-399.10.14359/12121 ↗

35. Ng, C. K., 2003, “Tendon Stress and Flexural Strength of Externally Prestressed Beams,” ACI Structural Journal, V. 100, No. 5, Sept.-Oct., pp. 644-653.10.14359/12806 ↗

36. Ozkul, O.; Nassif, H.; Tanchan, P.; and Harajli, M. H., 2008, “Rational Approach for Predicting Stress in Beams with Unbonded Tendons,” ACI Structural Journal, V. 105, No. 3, May-June, pp. 338-347.10.14359/19793 ↗

37. Pannell, F. N., 1969, “The Ultimate Moment of Resistance of Unbonded Prestressed Concrete Beams,” Magazine of Concrete Research, V. 21, No. 66, pp. 43-54. doi: 10.1680/macr.1969.21.66.4310.1680/macr.1969.21.66.43 ↗

38. Roberts-Wollmann, C. L.; Kreger, M. E.; Rogowsky, D. M.; and Breen, J. E., 2006, “Stresses in External Tendons at Ultimate,” ACI Structural Journal, V. 102, No. 2, Mar.-Apr., pp. 203-213.10.14359/14271 ↗

39. Tam, A., and Pannell, F. N., 1976, “The Ultimate Moment of Resistance of Unbonded Partially Prestressed Reinforced Concrete Beams,” Magazine of Concrete Research, V. 28, No. 97, pp. 203-208. doi: 10.1680/macr.1976.28.97.20310.1680/macr.1976.28.97.203 ↗

40. Thian-Poh, T., 1975, “Experimental Study of the Behavior of Simply Supported Unbonded Post-Tensioned One-Way Slabs,” master’s thesis, Department of Civil Engineering, University of Waterloo, Waterloo, ON, Canada.

41. Warwaruk, J.; Sozen, M. A.; and Siess, C. P., 1962, “Investigation of Prestressed Reinforced Concrete for Highway Bridges, Part III—Strength and Behavior in Flexure of Prestressed Concrete Beams (Engineering Experiment Station Bulletin No. 464),” University of Illinois, Urbana, IL.