Design Approach for Flexural Capacity of Prestressed Concrete Beams with External Tendons
Publication: Journal of Structural Engineering
Volume 144, Issue 12
Abstract
Due to a lack of bonds between external tendons and adjacent concrete and the potential variation in the eccentricities of the tendons (second-order effect), the analysis of the ultimate strength behavior of externally prestressed concrete (PC) beams is rather complicated. In this paper, a new design approach is proposed to calculate the flexural capacity of simply supported PC beams with external steel or fiber-reinforced polymer (FRP) tendons. First, an assumed deflected shape of a beam, which is supported by a comparison of experimental and analytical results, is incorporated into a beam–tendon structural deformation model to implement global deformation compatibility. In conjunction with sectional equilibrium and compatibility, simplified yet rational design equations are then developed to predict the ultimate stress increase in external tendons. Finally, a design approach that takes into account the second-order effect is proposed to calculate the flexural capacity of the beams. It is found, by comparing their predictions with available experimental results on 96 beams, that the proposed approach is more consistent and accurate than existing guidelines or models.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors gratefully acknowledge the financial support provided by the National Key R&D Program of China (2016YFC0701403), Natural Science Foundation of China (51678433), and the Project of Shanghai Science Technology Commission (16DZ1201802 and 16XD1402800). It should be mentioned that the presented design approach has been incorporated into the Chinese national standard, “Technical standard for FRP composites in construction,” and the Chinese national industrial standard, “Technical Standard for Concrete Bridge with FRP Reinforcements.”
References
AASHTO. 2014. Bridge design specifications. Washington, DC: AASHTO.
ACI (American Concrete Institute). 2004. Prestressing concrete structures with FRP tendons. ACI 440.4R-04. Farmington Hills, MI: ACI.
ACI (American Concrete Institute). 2014. Building code requirements for structural concrete and commentary. ACI 318-14. Farmington Hills, MI: ACI.
Alkhairi, F. M., and A. E. Naaman. 1993. “Analysis of beams prestressed with unbonded internal or external tendons.” J. Struct. Eng. 119 (9): 2680–2700. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:9(2680).
Aparicio, A. C., G. Ramos, and J. R. Casas. 2002. “Testing of externally prestressed concrete beams.” Eng. Struct. 24 (1): 73–84. https://doi.org/10.1016/S0141-0296(01)00062-1.
Ariyawardena, N., and A. Ghali. 2002. “Prestressing with unbonded internal or external tendons: Analysis and computer model.” J. Struct. Eng. 128 (12): 1493–1501. https://doi.org/10.1061/(ASCE)0733-445(2002)128:12(1493).
Au, F. T. K., R. K. L. Su, K. Tso, and K. H. E. Chan. 2008. “Behaviour of partially prestressed beams with external tendons.” Mag. Concr. Res. 60 (6): 455–467. https://doi.org/10.1680/macr.2008.60.6.455.
Bennitz, A., J. W. Schmidt, J. Nilimaa, P. Goltermann, and D. L. Ravn. 2012. “Reinforced concrete T-beams externally prestressed with unbonded carbon fiber-reinforced polymer tendons.” ACI Struct. J. 109 (4): 521–530. https://doi.org/10.1680/macr.2008.60.6.455.
Conti, E., R. Tardy, and M. Virlogeux. 1993. “Friction losses in some externally prestressed bridges in France.” In Proc., Workshop on Behaviour of External Prestressing in Structures, edited by E. Conti and R. Tardy. Bagneux, France: Association Française Pour la Construction.
Dall’Asta, A., and L. Dezi. 1998. “Nonlinear behavior of externally prestressed composite beams: Analytical model.” J. Struct. Eng. 124 (5): 588–597. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:5(588).
Dall’Asta, A., L. Ragni, and A. Zona. 2007a. “Analytical model for geometric and material nonlinear analysis of externally prestressed beams.” J. Eng. Mech. 133 (1): 117–121. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:1(117).
Dall’Asta, A., L. Ragni, and A. Zona. 2007b. “Simplified method for failure analysis of concrete beams prestressed with external tendons.” J. Struct. Eng. 133 (1): 121–131. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:1(121).
Dall’Asta, A., and A. Zona. 2005. “A finite element model for externally prestressed composite beams with deformable connection.” J. Struct. Eng. 131 (5): 706–714. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:5(706).
Du, J. S., D. Yang, P. L. Ng, and F. T. K. Au. 2011. “Response of concrete beams partially prestressed with external unbonded carbon fiber-reinforced polymer tendons.” Adv. Mater. Res. 150: 344–349. https://doi.org/10.4028/www.scientific.net/amr.150-151.344.
El-Refai, A., J. West, and K. Soudki. 2007. “Strengthening of RC beams with external posttensioned CFRP tendons.” In Case histories and use of FRP for prestressing applications, SP-245, 123–242. Farmington Hills, MI: American Concrete Institute.
Ghallab, A. 2013. “Calculating ultimate tendon stress in externally prestressed continuous concrete beams using simplified formulas.” Eng. Struct. 46: 417–430. https://doi.org/10.1016/j.engstruct.2012.07.018.
Ghallab, A., and A. W. Beeby. 2005. “Factors affecting the external prestressing stress in externally strengthened prestressed concrete beams.” Cem. Concr. Compos. 27 (9): 945–957. https://doi.org/10.1016/j.cemconcomp.2005.05.003.
Grace, N. F., and G. Abdel-Sayed. 2000. “Behavior of carbon fiber reinforced prestressed concrete skew bridges.” ACI Struct. J. 97 (1): 26–34. https://doi.org/10.14359/830.
Grace, N. F., M. Bebawy, and M. Kasabasic. 2015. Evaluation and analysis of decked bulb T beam bridge. Southfield, MI: Lawrence Technological Univ.
Harajli, M. 1993. “Strengthening of concrete beams by external prestressing.” PCI J. 38 (6): 76–88. https://doi.org/10.15554/pcij.11011993.76.88.
Harajli, M. 2006. “On the stress in unbonded tendons at ultimate: Critical assessment and proposed changes.” ACI Struct. J. 103 (6): 803–812. https://doi.org/10.14359/18231.
Harajli, M. 2011. “Proposed modification of AASHTO-LRFD for computing stress in unbonded tendons at ultimate.” J. Bridge Eng. 16 (6): 828–838. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000183.
Harajli, M., N. Khairallah, and H. Nassif. 1999. “Externally prestressed members: evaluation of second-order effects.” J. Struct. Eng. 125 (10): 1151–1161. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:10(1151).
He, Z. Q., and Z. Liu. 2010. “Stresses in external and internal unbonded tendons: Unified methodology and design equations.” J. Struct. Eng. 136 (9): 1055–1065. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000202.
Jung, W. T., J. S. Park, and Y. H. Park. 2013. “An experimental study on the flexural behavior of post-tensioned concrete beams with CFRP tendons.” Appl. Mech. Mater. 351–352: 717–721. https://doi.org/10.4028/www.scientific.net/AMM.351-352.717.
Karbhari, V. M. 1998. Use of composite materials in civil infrastructure in Japan. Baltimore: International Technology Research Institute.
Khairallah, N., and M. H. Harajli. 1997. Experimental and analytical evaluation of the behavior of concrete T beams with external prestressing. Beirut, Lebanon: American Univ. of Beirut.
Lee, L. H., J. H. Moon, and J. H. Lim. 1999. “Proposed methodology for computing of unbonded tendon stress at flexural failure.” ACI Struct. J. 96 (6): 1040–1048. https://doi.org/10.14359/781.
Lee, S. H., K. Shin, and T. H. K. Kang. 2014. “Non-iterative moment capacity equation for reinforced concrete beams with external post-tensioning.” ACI Struct. J. 111 (5): 1111–1122. https://doi.org/10.14359/51686815.
Lou, T. J., A. V. Lopes, and S. M. R. Lopes. 2012. “Influence of span-depth ratio on behavior of externally prestressed concrete beams.” ACI Struct. J. 109 (5): 687–695. https://doi.org/10.14359/51684046.
MacGregor, R. J. G. 1989. “Strength and ductility of externally posttensioned segmental box girders.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Texas at Austin.
Maguire, M., M. Chang, W. Collins, and Y. Sun. 2017. “Stress increase of unbonded tendons in continuous posttensioned members.” J. Bridge Eng. 22 (2): 04016115. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000991.
Mattock, A. H., J. Yamazaki, and B. Kattula. 1971. “Comparative study of prestressed concrete beams, with and without bond.” ACI J. 68 (2): 116–125. https://doi.org/10.14359/11298.
Mojtahedi, S., and W. Gamble. 1978. “Ultimate steel stress in unbonded prestressed concrete.” J. Struct. Div. 104 (7): 1159–1164.
Mutsuyoshi, H., K. Tsuchida, S. Matupayont, and A. Machida. 1995. “Flexural behavior and proposal of design equation for flexural strength of externally PC members.” Proc. JSCE 508 (26): 67–77. https://doi.org/10.2208/jscej.1995.508_67.
Naaman, A. E., and F. M. Alkhairi. 1991. “Stress at ultimate in unbonded post-tensioning tendons: Part 2—Proposed methodology.” ACI Struct. J. 88 (6): 683–692. https://doi.org/10.14359/1288.
Ng, C. K. 2003. “Tendon stress and flexural strength of externally prestressed beams.” ACI Struct. J. 100 (5): 644–653. https://doi.org/10.14359/12806.
Ng, C. K., and K. H. Tan. 2006. “Flexural behaviour of externally prestressed beams. Part II: Experimental investigation.” Eng. Struct. 28 (4): 622–633. https://doi.org/10.1016/j.engstruct.2005.09.016.
Niu, B. 1999. “The analysis of flexural behavior of externally prestressed concrete beams.” [In Chinese.] Chi. Civ. Eng. J. 32 (4): 37–44. https://doi.org/10.3321/j.issn:1000-131X.2000.03.002.
Roberts-Wollmann, C. L., M. E. Kreger, D. M. Rogowsky, and J. E. Breen. 2005. “Stresses in external tendons at ultimate.” ACI Struct. J. 102 (2): 206–213. https://doi.org/10.14359/14271.
Shin, K. J., and S. H. Lee. 2010. “Flexural behaviour of RC beams strengthened with high-tension steel rod.” Mag. Concr. Res. 62 (2): 137–147. https://doi.org/10.1680/macr.2008.62.2.137.
Shin, K. J., S. H. Lee, and H. K. Kang. 2014. “External posttensioning of reinforced concrete beams using a V-shaped steel rod system.” J. Struct. Eng. 140 (3): 04013067. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000824.
Tan, K. H., M. Abdullah-Al Farooq, and C. K. Ng. 2001. “Behavior of simple-span reinforced concrete beams locally strengthened with external tendons.” ACI Struct. J. 98 (2): 174–183. https://doi.org/10.14359/10185.
Tan, K. H., and C. K. Ng. 1997. “Effects of deviators and tendon configuration on behavior of externally prestressed beams.” ACI Struct. J. 94 (1): 13–22. https://doi.org/10.14359/456.
Wang, J. Q., Z. Liu, and Z. T. Lu. 2005. “Stress increment of prestressing tendons based on deflection for unbonded or external prestressed beams.” [In Chinese.] J. Southeast Univ. 35 (6): 915–919. https://doi.org/10.1016/j.engstruct.2015.06.052.
Wang, X., J. Shi, G. Wu, L. Yang, and Z. Wu. 2015. “Effectiveness of basalt FRP tendons for strengthening of RC beams through the external prestressing technique.” Eng. Struct. 101: 34–44. https://doi.org/10.1016/j.engstruct.2015.06.052.
Xue, W. C., F. Peng, Y. Tan, S. Zhang, K. Fu, and Y. Yang. 2016. “A review of studies on concrete structures with FRP reinforcements in China.” In Proc., 7th Int. Conf. on Advanced Composite Materials in Bridges and Structures. Vancouver, BC, Canada: Canadian Society for Civil Engineering.
Xue, W. C., X. H. Wang, and S. L. Zhang. 2008. “Bond properties of high-strength carbon fiber-reinforced polymer strands.” ACI Mater. J. 105 (1): 11–19. https://doi.org/10.14359/19202.
Zona, A., L. Ragni, and A. Dall’Asta. 2008. “Finite element formulation for geometric and material nonlinear analysis of beams prestressed with external slipping tendons.” Finite Elem. Anal. Des. 44 (15): 910–919. https://doi.org/10.1016/j.finel.2008.06.005.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 144 • Issue 12 • December 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Oct 24, 2017
Accepted: Jun 4, 2018
Published online: Sep 22, 2018
Published in print: Dec 1, 2018
Discussion open until: Feb 22, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.