Title:
End-Zone Reinforcing Schemes for Prestressed Concrete Bulb-Tee Girders
Author(s):
Yail J. Kim and Thi Ha
Publication:
Structural Journal
Volume:
123
Issue:
1
Appears on pages(s):
219-232
Keywords:
end zones; failure; prestressed concrete; reinforcing schemes
DOI:
10.14359/51749103
Date:
1/1/2026
Abstract:
This paper presents the effectiveness of various reinforcing schemes in the end zones of prestressed concrete bulb-tee girders. The default girder, provided by a local transportation agency, includes C-bars and spirals intended to control cracking, and is analyzed using three-dimensional finite element analysis. The formulated models are used to evaluate the breadth of end zones, strain responses, cracking patterns, damage amounts, and splitting forces, depending upon the configuration of the end-zone reinforcement. The number of C-bars is not influential in developing strand stress along the girder. The maximum principal stresses exceed the conventional limit within h/4 of the girder end, where h is the girder depth; however, the 3h/4 limit adequately encompasses the stress profiles, particularly in the web of the girder. The maximum tensile strain in the concrete varies with the elevation of the girder and the inclined strands cause local compression in the C-bars, while spiral strains are independent of the number of bars. By positioning the C-bars, the vertical strain of the concrete decreases by more than 15.9%, which can minimize crack formation. Whereas the short-term crack width of the girder may not be an immediate concern, its long-term width is found to surpass the established limit of 0.18 mm (0.007 in.). In this regard, multiple C-bars should be placed to address concerns about undesirable cracking. The splitting cracks in the girder, resulting from the strand angles and eccentricities, can be properly predicted by published specifications within the range of 0.2h to 0.7h, beyond which remarkable discrepancies are observed in comparison with a refined approach. From a practical perspective, two to three No. 6 or 7 C-bars spaced 150 mm (6 in.) apart are recommended in the end zones alongside welded wire fabric.
Related References:
1. Arab, A.; Badie, S. S.; Manzari, M. T.; Khaleghi, B.; Seguirant, S. J.; and Chapman, D., “Analytical Investigation and Monitoring of End-Zone Reinforcement of the Alaskan Way Viaduct Super Girders,” PCI Journal, V. 59, No. 2, 2014, pp. 109-128. doi: 10.15554/pcij.03012014.109.128
2. Yapar, O.; Basu, P. K.; and Nordendale, N., “Accurate Finite Element Modeling of Pretensioned Prestressed Concrete Beams,” Engineering Structures, V. 101, 2015, pp. 163-178. doi: 10.1016/j.engstruct.2015.07.018
3. AASHTO, AASHTO LRFD Bridge Design Specifications (9th Edition), American Association of State Highway and Transportation Officials, Washington, DC, 2020.
4. Salas, R. M.; Schokker, A. J.; West, J. S.; Breen, J. E.; and Kreger, M. E., “Corrosion Risk of Bonded, Post-Tensioned Concrete Elements,” PCI Journal, V. 53, No. 1, 2008, pp. 89-108. doi: 10.15554/pcij.01012008.89.108
5. Abdel-Jaber, H., and Glisic, B., “Monitoring of Prestressing Forces in Prestressed Concrete Structures—An Overview,” Structural Control and Health Monitoring, V. 26, No. 8, 2019, p. e2374. doi: 10.1002/stc.2374
6. Ross, B. E.; Willis, M. D.; Hamilton, H. R.; and Consolazio, G. R., “Comparison of Details for Controlling End-Region Cracks in Precast, Pretensioned Concrete I-Girders,” PCI Journal, V. 59, No. 2, 2014, pp. 96-108. doi: 10.15554/pcij.03012014.96.108
7. ACI Committee 224, “Control of Cracking in Concrete Structures (ACI 224R-01),” American Concrete Institute, Farmington Hills, MI, 2001, 46 pp.
8. PCI, PCI Manual for the Evaluation and Repair of Precast, Prestressed Concrete Bridge Products, Precast/Prestressed Concrete Institute, Chicago, IL, 2006.
9. Tadros, M. K., Badie, S. S.; and Tuan. C. Y., “Evaluation and Repair Procedures for Precast/Prestressed Concrete Girders with Longitudinal Cracking in the Web,” NCHRP Report 654, Transportation Research Board, Washington, DC, 2010.
10. Steinberg, E., and Semendary, L., “Evaluation of Revised Details of End Zone of the Prestressed Concrete I-Girders Using Finite Element Method,” Structure and Infrastructure Engineering, V. 13, No. 11, 2017, pp. 1390-1403. doi: 10.1080/15732479.2016.1271437
11. Yao, G.; Xiong, X.; and Ge, Y., “Cracking Behavior of Full-Scale Pre-Tensioned Prestressed Concrete Double-Tee Members with Steel-Wire Meshes,” Journal of Building Engineering, V. 44, 2021, p. 102658. doi: 10.1016/j.jobe.2021.102658
12. Xiong, X.; Zhang, Y.; Ge, Y.; Shi, H.; Musa, M. M. E.; and Yao, G., “Shear Behavior of Full-Scale Prestressed Concrete Double Tee Beams with Steel-Wire Meshes,” Journal of Building Engineering, V. 64, 2023, p. 105464. doi: 10.1016/j.jobe.2022.105464
13. Guyon, Y., “Prestressed Concrete,” Contractors Record, London, UK, 1955.
14. Marshall, W. T., and Mattock, A. H., “Control of Horizontal Cracking in the Ends of Pretensioned Prestressed Concrete Girders,” PCI Journal, V. 7, No. 5, 1962, pp. 56-74. doi: 10.15554/pcij.10011962.56.74
15. PCI, PCI Design Handbook, eighth edition, Precast/Prestressed Concrete Institute, Chicago, IL, 2017.
16. CDOT, CDOT Bridge Design Manual, Colorado Department of Transportation, Denver, CO, 2022.
17. MNL-133-23, “PCI Bridge Design Manual,” Precast/Prestressed Concrete Institute, Chicago, IL, 2023.
18. Hordijk, D. A., “Tensile and Tensile Fatigue Behavior of Concrete: Experiments, Modeling and Analyses,” Heron, V. 37, No. 1, 1992, pp. 3-79.
19. fib, “Model Code 2010,” Thomas Telford, London, UK, 2010.
20. Alfarah, B.; Lopez-Almansa, F.; and Oller, S., “New Methodology for Calculating Damage Variables Evolution in Plastic Damage Model for RC Structures,” Engineering Structures, V. 132, 2017, pp. 70-86. doi: 10.1016/j.engstruct.2016.11.022
21. Krätzig, W. B., and Polling, R., “An Elasto-Plastic Damage Model for Reinforced Concrete with Minimum Number of Material Parameters,” Computers & Structures, V. 82, No. 15-16, 2004, pp. 1201-1215. doi: 10.1016/j.compstruc.2004.03.002
22. ABAQUS, “Theory Manual,” Dassault Systemes, Velizy-Villacoublay, France, 2016.
23. Garg, A. K., and Abolmaali, A., “Finite-Element Modeling and Analysis of Reinforced Concrete Box Culverts,” Journal of Transportation Engineering, ASCE, V. 135, No. 3, 2009, pp. 121-128. doi: 10.1061/(ASCE)0733-947X(2009)135:3(121)
24. fib, Structural Concrete: Textbook on Behaviour, Design and Performance, International Federation for Structural Concrete, Lausanne, Switzerland, 2009.
25. Ren, W.; Sneed, L. H.; Yang, Y.; and He, R., “Numerical Simulation of Prestressed Precast Concrete Bridge Deck Panels Using Damage Plasticity Model,” International Journal of Concrete Structures and Materials, V. 9, No. 1, 2015, pp. 45-54. doi: 10.1007/s40069-014-0091-2
26. Boulbes, R. J., Troubleshooting Finite-Element Modeling with Abaqus with Application in Structural Engineering Analysis, Springer, Berlin, Germany, 2019.
27. O’Callaghan, M. R., and Bayrak, O., “Tensile Stresses in the End Zone Regions of Pretensioned I-Beams at Release,” Technical Report: IAC-88-5DD1A003-1, Texas Department of Transportation, Austin, TX, 2008.
28. Williams, M. S., and Sexsmith, R. G., “Seismic Damage Indices for Concrete Structures: A State-of-the-Art Review,” Earthquake Spectra, V. 11, No. 2, 1995, pp. 319-349. doi: 10.1193/1.1585817
29. Ugural, A. C., and Fenster, S. K., Advanced Strength and Applied Elasticity, third edition, Prentice-Hall, Hoboken, NJ, 1995.
30. Ronanki, V. S.; Burkhalter, D. I.; Aaleti, S.; Song, W.; and Richardson, J. A., “Experimental and Analytical Investigation of End Zone Cracking in BT-78 Girders,” Engineering Structures, V. 151, 2017, pp. 503-517. doi: 10.1016/j.engstruct.2017.08.014
31. Miura, T.; Sato, K.; and Nakamura, H., “The Role of Microcracking on the Compressive Strength and Stiffness of Cracked Concrete with Different Crack Widths and Angles Evaluated by DIC,” Cement and Concrete Composites, V. 114, 2020, p. 103768. doi: 10.1016/j.cemconcomp.2020.103768
32. EN 1992-1-1:2004, “Eurocode 2: Design of Concrete Structures,” European Committee for Standardization, Brussels, Belgium, 2004.
33. ACI Committee 209, “Guide for Modeling and Calculating Shrinkage and Creep in Hardened Concrete (ACI 209.2R-08),” American Concrete Institute, Farmington Hills, MI, 2008, 45 pp.
34. Leonhardt, F., “Cracks and Crack Control in Concrete Structures,” PCI Journal, V. 33, No. 4, 1988, pp. 124-145. doi: 10.15554/pcij.07011988.124.145
35. Wang, J.; Basheer, P. A. M.; Nanukuttan, S. V.; Long, A. E.; and Bai, Y., “Influence of Service Loading and the Resulting Micro-Cracks on Chloride Resistance of Concrete,” Construction and Building Materials, V. 108, 2016, pp. 56-66. doi: 10.1016/j.conbuildmat.2016.01.005
36. Ferreira, T., and Rashband, W., “The ImageJ User Guide,” National Institute of Health, Bethesda, MD, 2012.
37. ACI Committee 302, “Guide to Concrete Floor and Slab Construction (ACI 302.1R-15),” American Concrete Institute, Farmington Hills, MI, 2015, 76 pp.
38. He, Z.-Q., and Liu, Z., “Investigation of Bursting Forces in Anchorage Zones: Compression-Dispersion Models and Unified Design Equation,” Journal of Bridge Engineering, ASCE, V. 16, No. 6, 2011, pp. 820-827. doi: 10.1061/(ASCE)BE.1943-5592.0000187
39. Mertz, D. R., “AASHTO LRFD 2008 Interim Changes,” Aspire, V. 2, No. 1, 2008, p. 56.