Tendon Profile Layout Impact on the Shear Capacity of Unbonded Post-Tensioned Prestressed Concrete Bridge I-Girders
Abstract
1. Introduction
2. Materials and Methods
2.1. Concrete Mix Design and Material Properties
2.2. Specimen’s Shape, Size, and Dimensions
2.3. Prestressing and Reinforcement Details
2.4. Tested Specimens’ Preparation
2.5. Experimental Variables
2.6. Test Setup and Instrumentation
2.7. Experimental Procedure
3. Experimental Program
3.1. Load–Deflection Curves
3.2. Crack Patterns and Mode of Failure
4. Conclusions
- The tendon profile layout significantly influenced the failure process in unbonded prestressed concrete I-girders.
- The shear behavior of the specimens was characterized by three stages: the elastic stage, the elastic–plastic stage, and the plastic (ductility) stage. All specimens experienced shear failure.
- The first cracks occurred at approximately 20.83% to 30.11% of the ultimate load, averaging around 26.17% for all specimens.
- Among the specimens with a trapezoidal tendon profile, the greater increase in ultimate load was observed in specimen GS-4 TR, which showed a 7.64% improvement compared to the control beam. For the specimens with a parabolic tendon profile, an increase of 3.8% in ultimate load was recorded, with specimen GS-7 PR achieving a maximum increase of 22.83 kN over the control beam. Specimens featuring a harped tendon profile also demonstrated a greater increase in ultimate load, with specimen GS-3 HA showing a significant 17.52 improvement over the control beam. The specimen GS-3 HA with a harped tendon profile showed the highest ultimate load in comparison with all other tendon profiles. These results highlight the beneficial impact of tendon profile layout on the load-carrying capacity of prestressed concrete beams.
- The vertical deflection measurements of the tendon profile specimens revealed distinct variations. For the trapezoidal tendon profile, specimen GS-3 TR exhibited the smallest ultimate load deflection at 37.59 mm, which was 24.88% greater than that of the GS-1 ST. Among the parabolic tendon profile specimens, GF-5 PR showed the lowest ultimate load deflection at 37.24 mm, 22.56% higher than GS-1 ST, while for the harped tendon profile, GS-1 HA recorded a lower ultimate load deflection of 35.82 mm, 19% greater than GS-1 ST. The specimen GS-1 HA with a harped tendon profile showed the lowest ultimate load deflection in comparison with the trapezoidal and parabolic tendon profiles. These findings highlight the influence of tendon profile shapes on ultimate load deflection, offering insights into their structural performance.
- This study revealed that each tendon profile shape (trapezoidal, parabolic, harped) exhibited the highest ultimate load capacity and ultimate load deflection when beams had higher eccentricity (80 mm above N.A.), while beams with lower eccentricity (80 mm below N.A.) resulted in the lowest load capacity and ultimate load deflection. Notably, specimen GS-3 HA, featuring the harped tendon profile, displayed the greatest ultimate load capacity, while specimen GS-1 HA, with the harped tendon profile, recorded the smallest ultimate load deflection. These findings highlight the significant influence of tendon profile shape and eccentricity on the structural performance of the specimens.
- The experimental results of girders tested with optimized tendon profiles indicated that their performance was enhanced remarkably in comparison with the control beam and the harped tendon profile showed the best improvements in performance in comparison with all other tendon profiles. These girders could carry higher loads, and these girders could sustain larger loads due to the more effective distribution of the prestressing forces along the girder length. The optimum tendon arrangements led to the more homogeneous distribution of stresses inside the concrete, fully utilizing a larger part of the cross-section. This study demonstrates the advantage of adopting optimized tendon profiles to enhance the performance of prestressed concrete bridge girders.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Darwin, D.; Dolan, C.W. Design of Concrete Structures, 16th ed.; McGraw-Hill Education: Columbus, OH, USA, 2021; ISBN 9781260575118. [Google Scholar]
- Hao, H.; Bi, K.; Chen, W.; Pham, T.M.; Li, J. Towards next Generation Design of Sustainable, Durable, Multi-Hazard Resistant, Resilient, and Smart Civil Engineering Structures. Eng. Struct. 2023, 277, 115477. [Google Scholar] [CrossRef]
- Nilson, A.H. Design of Prestressed Concrete, 2nd ed.; Wiley: Hoboken, NJ, USA, 1987. [Google Scholar]
- Naser, A.F.; Zonglin, W. Strengthening of Jiamusi Pre-Stressed Concrete Highway Bridge by Using External Post-Tensioning Technology in China. J. Eng. Appl. Sci. 2010, 5, 60–69. [Google Scholar]
- Naser, A.F.; Zonglin, W. Finite Element and Experimental Analysis and Evaluation of Static and Dynamic Responses of Oblique Pre-Stressed Concrete Box Girder Bridge. Res. J. Appl. Sci. Eng. Technol. 2013, 6, 3642–3657. [Google Scholar] [CrossRef]
- Abdullah, A.B.M.; Rice, J.A.; Hamilton, H.R.; Consolazio, G.R. Damage Identification in Unbonded Tendons for Post-Tensioned Bridges. In Proceedings of the International Conference on Advances in Experimental Structural Engineering, Urbana, IL, USA, 1–2 August 2015; p. 8. [Google Scholar]
- Corven, J.; Natio, C.; Pessiki, S. Designing and Detailing Post-Tensioned Bridges to Accommodate Nondestructive Evaluation; Federal Highway Administration: Washington, DC, USA, 2018. [Google Scholar]
- Fuzier, J.-P.; Ganz, H.-R.; Matt, P. Durability of-Tensioning Tendons; Case Postale 88, CH-1015; International Federation for Structural Concrete: Lausanne, Switzerland, 2006. [Google Scholar]
- Nusrath, F.R.; Satheesh, V.S.; Manigandan, M.; Suresh, B.S. An Overview on Tendon Layout for Prestressed Concrete Beams. Int. J. Innov. Sci. Eng. Technol. 2015, 2, 944–949. [Google Scholar]
- Rupf, M.; Fernández Ruiz, M.; Muttoni, A. Post-Tensioned Girders with Low Amounts of Shear Reinforcement: Shear Strength and Influence of Flanges. Eng. Struct. 2013, 56, 357–371. [Google Scholar] [CrossRef]
- Huber, P.; Huber, T.; Kollegger, J. Experimental and Theoretical Study on the Shear Behavior of Single- and Multi-Span T- and I-Shaped Post-Tensioned Beams. Struct. Concr. 2019, 21, 393–408. [Google Scholar] [CrossRef]
- Ruiz, M.F.; Muttoni, A. Shear Strength of Thin-Webbed Post-Tensioned Beams. ACI Struct. J. 2008, 105, 308–317. [Google Scholar]
- Rana, S.; Ahsan, R. Design of Prestressed Concrete I-Girder Bridge Superstructure Using Optimization Algorithm. IABSE-JSCE Jt. Conf. Adv. Bridge Eng.-II 2010, 211–223. [Google Scholar]
- Huber, P.; Wien, T.U.; Huber, T.; Kollegger, J. Shear Behavior of Post-Tensioned Concrete Beams with a Low Amount of Transverse Reinforcement. In Proceedings of the Fib Symposium 2016 Cape Town, Cape Town, South Africa, 1 November 2016. [Google Scholar]
- Hillebrand, M.; Hegger, J. Fatigue Testing of Shear Reinforcement in Prestressed Concrete T-Beams of Bridges. Appl. Sci. 2020, 10, 5560. [Google Scholar] [CrossRef]
- Eisa, A.S.; Kotrasova, K.; Sabol, P.; Mihaliková, M.; Attia, M.G. Experimental and Numerical Study of Strengthening Prestressed Reinforced Concrete Beams Using Different Techniques. Buildings 2024, 14, 29. [Google Scholar] [CrossRef]
- Qi, H.; Jiang, H.; Wang, B.; Zhuge, P. Experimental Study on Shear Performance of Concrete Beams Reinforced with Externally Unbonded Prestressed CFRP Tendons. Fibers 2024, 12, 23. [Google Scholar] [CrossRef]
- Zhao, K.; Wang, H.; Li, H.; Wei, Y.; Lu, J.; Li, G. Experimental and Numerical Analysis of Shear Performance of 16 m Full-Scale Prestressed Hollow Core Slabs. Infrastructures 2025, 10, 2. [Google Scholar] [CrossRef]
- Jancy, A.; Stolarski, A.; Zychowicz, J. Experimental and Numerical Research of Post-Tensioned Concrete Beams. Materials 2023, 16, 4141. [Google Scholar] [CrossRef]
- Lim, H.-S.; Jun, B.-K.; Shin, D.-I.; Lee, J.-Y. Shear Capacity of Post-Tensioning Pre-Stressed Concrete Beams with High Strength Stirrups. Int. J. Struct. Civ. Eng. Res. 2016, 4, 258–264. [Google Scholar] [CrossRef]
- Yaqub, M.A.; Czaderski, C.; Matthys, S. Shear Strengthening of Precast Prestressed Bridge I-Girders Using Shape Memory Reinforcement. Eng. Struct. 2024, 305, 117743. [Google Scholar] [CrossRef]
- Wang, L.; Hu, Z.; Yi, J.; Dai, L.; Ma, Y.; Zhang, X. Shear Behavior of Corroded Post-Tensioned Prestressed Concrete Beams with Full/Insufficient Grouting. KSCE J. Civ. Eng. 2020, 24, 1881–1892. [Google Scholar] [CrossRef]
- Peng, F.; Xue, W. Experimental Investigation on Shear Behavior of FRP Post-Tensioned Concrete Beams without Stirrups. Eng. Struct. 2021, 244, 112835. [Google Scholar] [CrossRef]
- Qi, J.; Ma, Z.J.; Wang, J.; Bao, Y. Post-Cracking Shear Behaviour of Concrete Beams Strengthened with Externally Prestresssed Tendons. Structures 2020, 23, 214–224. [Google Scholar] [CrossRef]
- Jiang, C.; Xiong, W.; Ye, J. Simplified Design Formula for the Shear Capacity of Prestressed Concrete T-Beams Strengthened by Steel Plates. KSCE J. Civ. Eng. 2025, 29, 100013. [Google Scholar] [CrossRef]
- Ahmed, G.H.; Aziz, O.Q. Shear Behavior of Dry and Epoxied Joints in Precast Concrete Segmental Box Girder Bridges under Direct Shear Loading. Eng. Struct. 2019, 182, 89–100. [Google Scholar] [CrossRef]
- Ahmed, G.H.; Aziz, O.Q. Influence of Intensity & Eccentricity of Posttensioning Force and Concrete Strength on Shear Behavior of Epoxied Joints in Segmental Box Girder Bridges. Constr. Build. Mater. 2019, 197, 117–129. [Google Scholar] [CrossRef]
- Ma, G.; Wu, Y.; Hwang, H.J.; Shi, C. Database Evaluation of Shear Strength of Prestressed Concrete Beams. Structures 2025, 73, 108288. [Google Scholar] [CrossRef]
- Ng, P.L.; Kwan, A.K.H. Practical Determination of Prestress Tendon Profile by Load-Balancing Method. HKIE Trans. Hong Kong Inst. Eng. 2006, 13, 27–35. [Google Scholar] [CrossRef]
- Jagarapu, D.C.K.; Venkat, L. Genetic Algorithm Based Optimum Design of Prestressed Concrete Beam. Int. J. Comput. Civ. Struct. Eng. 2013, 3, 644–654. [Google Scholar] [CrossRef]
- Khan, A.A.; Pathak, K.K.; Dindorkar, N. Cable Layout Design of One Way Prestressed Slabs Using Fem. J. Eng. Sci. Manag. Educ. 2010, 2, 34–41. [Google Scholar]
- Colajanni, P.; Recupero, A.; Spinella, N. Design Procedure for Prestressed Concrete Beams. Comput. Concr. 2014, 13, 235–253. [Google Scholar] [CrossRef]
- Dixit, A.S.; Khurd, V.G. Effect of Prestressing Force, Cable Profile and Eccentricity on Post Tensioned Beam. Int. Res. J. Eng. Technol. 2017, 4, 626–632. [Google Scholar]
- Naser, A.F. Optimum Design of Vertical Steel Tendons Profile Layout of Post-Tensioning Concrete Bridges: Fem Static Analysis. ARPN J. Eng. Appl. Sci. 2018, 13, 9244–9256. [Google Scholar]
- Mihaylov, B.I.; Liu, J.; Simionopoulos, K.; Bentz, E.C.; Collins, M.P. Effect of Member Size and Tendon Layout on Shear Behavior of Post-Tensioned Beams. ACI Struct. J. 2019, 116, 265–274. [Google Scholar] [CrossRef]
- Yakov, Z.; Amir, O. Layout Optimization of Post-Tensioned Cables in Concrete Slabs. Struct. Multidiscip. Optim. 2021, 63, 1951–1974. [Google Scholar] [CrossRef]
- Rani, U.M. Effect of Tendon Profile on Deflections in Prestressed Concrete Beams Using C Programme. Int. J. Comput. Sci. Eng. 2021, 8, 6–8. [Google Scholar] [CrossRef]
- Mohamed, G.A.; Eisa, A.S.; Purcz, P.; Ručinský, R.; El-Feky, M.H. Effect of External Tendon Profile on Improving Structural Performance of RC Beams. Buildings 2022, 12, 789. [Google Scholar] [CrossRef]
- Huber, P.; Wien, T.U.; Huber, P.; Kollegger, J. Shear Strength of Post-Tensioned Concrete Girders with Minimum Shear Reinforcement. In Proceedings of the 11th CCC Congress, Hainburg, Austria, 1–2 September 2015. [Google Scholar]
- ACI Committee 318. Building Code Requirements for Structural Concrete (ACI 318-19) Commentary on Building Code Requirements for Structural Concrete (ACI 318R-19); American Concrete Institute: Farmington Hills, MI, USA, 2019. [Google Scholar]
- American Concrete Institute Committee 211. Selecting Proportions for Normal-Density and High-Density Concrete-Guide Inch-Pound Units Selecting Proportions for Normal-Density and High-Density Concrete-Guide; American Concrete Institute: Farmington Hills, MI, USA, 2022. [Google Scholar]
- British Standards Institution. Part 3, Compressive Strength of Test Specimens. In Testing Hardened Concrete; British Standards Institution: London, UK, 2019; ISBN 9780580984426. [Google Scholar]
- ASTM C496/C496M-17; Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens (ASTM C496/C496M-17). ASTM International: West Conshohocken, PA, USA, 2017; Volume 04.02.
- Fakhrulddin Abdullah, A.; Burhan Al-Deen Abdul-Rahman, M.; Abbas Al-Attar, A. Investigate the Mechanical Characteristics and Microstructure Of-Geopolymer Concrete Exposure to High Temperatures. J. Rehabil. Civ. Eng. 2025, 14, 2141. [Google Scholar]
- Husain, H.M.; Oukaili, N.K.; Jomaa’h, M.M. Effect of Prestressing Force on Torsion Resistance of Concrete Beams. J. Eng. 2007, 13, 1902–1918. [Google Scholar]
- ASTM C469/C469M-14; Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression (ASTM C469/C469M-14). ASTM International: West Conshohocken, PA, USA, 2014; Volume 04.02.
- ASTM A416/A416M-24; Standard Specification for Low-Relaxation Seven-Wire Steel Strand for Prestressed Concrete. ASTM International: West Conshohocken, PA, USA, 2024; Volume 01.04.
- ASTM A615/A615M-15a; Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete. ASTM International: West Conshohocken, PA, USA, 2015; Volume 01.04.
- ASTM A1064/A1064M-18a; Standard Specification For-Steel Wire and Welded Wire Reinforcement, Plain and Deformed, for Concrete1. ASTM International: West Conshohocken, PA, USA, 2018; Volume 01.04.
Materials | Quantities |
---|---|
Cement (g) | 425 |
Water (L) | 160 |
Additive (L) | 4 |
Fine Aggregate (kg) | 880 |
Coarse Aggregate (kg) | 910 |
W/C | 0.38 |
Slump (mm) | 150–180 |
Maximum Aggregate Size (mm) | 19 |
Type | Diameter (mm) | Area (mm2) | Yield Stress (MPa) | Ultimate Strength (MPa) | Maximum Elongation (%) | Modulus of Elasticity (MPa) | Standard |
---|---|---|---|---|---|---|---|
Strand | 15.26 | 140.54 | - | 2018 | 4.28 | 196,370 | ASTM A416/A416M [47] |
Deformed bar | 15.66 | 194.27 | 605 | 696 | 19 | 200,000 | ASTM A615/A615M [48] |
Deformed bar | 11.74 | 108.28 | 595 | 673 | 20 | 200,000 | ASTM A615/A615M [48] |
Steel wire | 4.37 | 15 | 700 | 710 | - | 200,000 | ASTM A1068/A1068M [49] |
Number of Specimens | Name of the Specimens | Name of Tendon Profile | Tendon Profile Layout, Units in (mm) |
---|---|---|---|
Specimen 1 | GS-1 ST | Straight Tendon Profile With e = 180 mm | |
Specimen 2 | GS-2 TR | Trapezoidal Tendon Profile With ee = +80 mm | |
Specimen 3 | GS-3 TR | Trapezoidal Tendon Profile With ee = 0 mm | |
Specimen 4 | GS-4 TR | Trapezoidal Tendon Profile With ee = −80 mm | |
Specimen 5 | GS-5 PR | Parabolic Tendon Profile With ee = +80 mm | |
Specimen 6 | GS-6 PR | Parabolic Tendon Profile With ee = 0 mm | |
Specimen 7 | GS-7 PR | Parabolic Tendon Profile With ee = −80 mm | |
Specimen 8 | GS-1 HA | Harped Tendon Profile With ee = +80 mm | |
Specimen 9 | GS-2 HA | Harped Tendon Profile With ee = 0 mm | |
Specimen 10 | GS-3 HA | Harped Tendon Profile With ee = −80 mm |
Specimen Name | First Crack Load (kN) | First Crack Deflection (mm) | Ultimate Load (kN) | Ultimate Load Deflection (mm) | Pcr/Pu % | Failure Mode |
---|---|---|---|---|---|---|
PCR | ∆CR | Pu | ∆u | |||
GS-1 ST | 167.17 | 1.36 | 601.17 | 30.1 | 27.81% | Shear a |
GS-2 TR | 137.98 | 0.98 | 603.03 | 42.59 | 22.88% | Shear a |
GS-3 TR | 184.73 | 0.79 | 613.42 | 37.59 | 30.11% | Shear a |
GS-4 TR | 188.72 | 1.44 | 647.08 | 42 | 29.16% | Shear a |
GS-5 PR | 178.60 | 2 | 607.43 | 37.24 | 29.40% | Shear a |
GS-6 PR | 183.95 | 1.68 | 613.60 | 42.04 | 29.98% | Shear a |
GS-7 PR | 151.20 | 1.43 | 624 | 42.46 | 24.23% | Shear a |
GS-1 HA | 126.73 | 0.86 | 608.40 | 35.82 | 20.83% | Shear a |
GS-2 HA | 145.88 | 1.30 | 615 | 41.95 | 23.72% | Shear a |
GS-3 HA | 166.48 | 1.52 | 706.5 | 43.81 | 23.56% | Shear a |
Compared Specimen | Increase in Ultimate Load | Increase in Ultimate Load Deflection | ||
---|---|---|---|---|
(kN) | % | (mm) | % | |
GS-1 ST and GS-2 TR | 1.86 | 0.31% | 12.49 | 41.50% |
GS-1 ST and GS-3 TR | 12.25 | 2.04% | 7.49 | 24.88% |
GS-1 ST and GS-4 TR | 45.91 | 7.64% | 11.9 | 39.53% |
GS-1 ST and GS-5 PR | 6.26 | 1.04% | 6.79 | 22.56% |
GS-1 ST and GS-6 PR | 12.43 | 2.07% | 11.94 | 39.67% |
GS-1 ST and GS-7 PR | 22.83 | 3.80% | 12.36 | 41.06% |
GS-1 ST and GS-1 HA | 7.23 | 1.20% | 5.72 | 19.00% |
GS-1 ST and GS-2 HA | 13.83 | 2.30% | 11.85 | 39.37% |
GS-1 ST and GS-3 HA | 105.33 | 17.52% | 13.71 | 45.55% |
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Hasib, S.I.; Lateef, A.M.; Aziz, O.Q. Tendon Profile Layout Impact on the Shear Capacity of Unbonded Post-Tensioned Prestressed Concrete Bridge I-Girders. Infrastructures 2025, 10, 222. https://doi.org/10.3390/infrastructures10090222
Hasib SI, Lateef AM, Aziz OQ. Tendon Profile Layout Impact on the Shear Capacity of Unbonded Post-Tensioned Prestressed Concrete Bridge I-Girders. Infrastructures. 2025; 10(9):222. https://doi.org/10.3390/infrastructures10090222
Chicago/Turabian StyleHasib, Swar I., Assim M. Lateef, and Omar Q. Aziz. 2025. "Tendon Profile Layout Impact on the Shear Capacity of Unbonded Post-Tensioned Prestressed Concrete Bridge I-Girders" Infrastructures 10, no. 9: 222. https://doi.org/10.3390/infrastructures10090222
APA StyleHasib, S. I., Lateef, A. M., & Aziz, O. Q. (2025). Tendon Profile Layout Impact on the Shear Capacity of Unbonded Post-Tensioned Prestressed Concrete Bridge I-Girders. Infrastructures, 10(9), 222. https://doi.org/10.3390/infrastructures10090222