Analytical Approach to the Torsional Behavior of Concrete Beams Reinforced with Fiber-Reinforced Polymer Bars

Cao Thanh Ngoc Tran; Vinh Sang Nguyen

doi:10.46604/aiti.2026.16061

Authors

Cao Thanh Ngoc Tran School of Civil Engineering and Management, International University, Ho Chi Minh City, Vietnam/ Vietnam National University, Ho Chi Minh City, Vietnam
Vinh Sang Nguyen Faculty of Civil Engineering, Thuyloi University, Hanoi, Vietnam

DOI:

https://doi.org/10.46604/aiti.2026.16061

Keywords:

torsion behavior, beam, FRP bars, modified softened membrane model for torsion

Abstract

Fiber-reinforced polymer (FRP) bars have emerged as a promising alternative to conventional steel reinforcement for improving the durability of reinforced concrete (RC) members in corrosive environments. Despite increasing experimental research, analytical models capable of capturing the pure torsional response of FRP bar-reinforced concrete beams remain scarce. This study presents a modified softened membrane model for torsion (SMMT) for solid FRP-RC beams. The proposed formulation incorporates an FRP-compatible strain-coupling relationship through a modified Hsu/Zhu approach to account for poisson’s effect. The model is validated against sixteen rectangular FRP-RC beam tests reported in the literature. Predicted cracking torque, ultimate torque, torque-twist response, and selected stirrup strain responses show good agreement with experimental results. A parametric study is further conducted to quantify the influences of concrete strength, FRP elastic modulus, and longitudinal and transverse FRP reinforcement ratios. The proposed model provides a reliable analytical framework for evaluating the torsional behavior of FRP-RC beams.

References

H. M. Mohamed and B. Benmokrane, "Design and Performance of Reinforced Concrete Water Chlorination Tank Totally Reinforced with GFRP Bars: Case Study," Journal of Composites for Construction, vol. 18, no. 1, article no. 05013001, 2014.

ACI Committee 440, "Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars (ACI 440.1R-06)," Farmington Hills, MI, USA: American Concrete Institute, 2006.

JSCE, "Recommendations for Upgrading of Concrete Structures with Use of Continuous Fiber Sheets," Japanese Society of Civil Engineers, Tokyo, Japan, 2001.

Canadian Standards Association (CSA), "Design of Concrete Structures (CAN/CSA-A23.3-94)," Rexdale, ON, Canada, 1994.

A. Deifalla, M. Hamed, A. Saleh, and T. Ali, "Exploring GFRP Bars as Reinforcement for Rectangular and L-Shaped Beams Subjected to Significant Torsion: An Experimental Study," Engineering Structures, vol. 59, pp. 776-786, 2014.

V. S. Nguyen, X. H. Nguyen, D. D. Le, C. T. N. Tran, and A. D. Nguyen, "Experimental Studies on Torsional Behavior of Reinforced Concrete Beams Strengthened Using Hybrid Carbon and Basalt FRP Sheets," Structural Concrete, vol. 26, no. 5, pp. 6594-6618, 2025.

I. T. Mostafa, S. Mousa, H. M. Mohamed, and B. Benmokrane, "Strength and Behavior of Glass Fiber-Reinforced Polymer-Reinforced Concrete Box Girders without Web Reinforcement under Pure Torsion," ACI Structural Journal, vol. 120, no. 5, pp. 63-76, 2023.

O. Chaallal, H. M. Mohamed, and B. Benmokrane, "Torsional Moment Capacity and Failure Mode Mechanisms of Concrete Beams Reinforced with Carbon FRP Bars and Stirrups," Journal of Composites for Construction, vol. 19, no. 2, article no. 04014049, 2015.

D. Li, Y. Lei, L. Jin, and X. Du, "Experimental Study on Torsional Size Effect of BFRP Bars-RC Beams," Engineering Structures, vol. 326, article no. 119595, 2025.

Canadian Standards Association (CSA), "Design of Concrete Structures (CAN/CSA-A23.3-04)," Mississauga, ON, Canada, 2004.

ACI Committee 318, "Building Code Requirements for Structural Concrete (ACI 318-05)," Farmington Hills, MI, USA: American Concrete Institute, 2005.

Canadian Standards Association (CSA), "Design and Construction of Building Structures with Fibre-Reinforced Polymers (CAN/CSA-S806-12)," Toronto, ON, Canada, 2012.

E. Rausch, Berechnung des Eisenbetons gegen Verdrehung (Torsion) und Abscheren. Berlin, Germany: Springer, 1938.

F. J. Vecchio and M. P. Collins, "The Modified Compression-Field Theory for Reinforced Concrete Elements Subjected to Shear," ACI Journal Proceedings, vol. 83, no. 2, pp. 219-231, 1986.

L. F. A. Bernardo and S. M. R. Lopes, "Behaviour of Concrete Beams under Torsion: NSC Plain and Hollow Beams," Materials and Structures, vol. 41, no. 6, pp. 1143-1167, 2008.

D. Mitchell and M. P. Collins, "Diagonal Compression Field Theory-A Rational Model for Structural Concrete in Pure Torsion," ACI Journal Proceedings, vol. 71, no. 8, pp. 396-408, 1974.

K. N. Rahal and M. P. Collins, "Combined Torsion and Bending in Reinforced and Prestressed Concrete Beams," ACI Structural Journal, vol. 100, no. 2, pp. 157-165, 2003.

T. T. C. Hsu and Y. L. Mo, "Softening of Concrete in Torsional Members-Theory and Tests," ACI Journal Proceedings, vol. 82, no. 3, pp. 290-303, 1985.

C. E. Chalioris, "Behaviour Model and Experimental Study for the Torsion of Reinforced Concrete Members," WIT Transactions on the Built Environment, vol. 85, pp. 459-468, 2006.

T. T. C. Hsu and R. R. H. Zhu, "Softened Membrane Model for Reinforced Concrete Elements in Shear," ACI Structural Journal, vol. 99, no. 4, pp. 460-469, 2002.

C. H. Jeng and T. T. C. Hsu, "A Softened Membrane Model for Torsion in Reinforced Concrete Members," Engineering Structures, vol. 31, no. 9, pp. 1944-1954, 2009.

R. R. H. Zhu and T. T. C. Hsu, "Poisson Effect in Reinforced Concrete Membrane Elements," ACI Structural Journal, vol. 99, no. 5, pp. 631-640, 2002.

A. D. Nguyen, V. S. Nguyen, X. H. Nguyen, D. D. Le, and C. T. N. Tran, "Softened Membrane Model for Forecasting Torsional Response of Reinforced Concrete Beams Strengthened Using FRP Sheets," Advances in Structural Engineering, vol. 28, no. 16, pp. 3019-3043, 2025.

T. T. C. Hsu, Unified Theory of Reinforced Concrete. Boca Raton, FL, USA: CRC Press, 1993.

T. T. C. Hsu and Y. L. Mo, Unified Theory of Concrete Structures. West Sussex, UK: John Wiley & Sons, 2010.

ACI Committee 440, "Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars (ACI 440.1R-15)," Farmington Hills, MI, USA: American Concrete Institute, 2015.

The MathWorks, Inc., MATLAB R2023a. Natick, MA, USA, 2023.

H. M. Mohamed and B. Benmokrane, "Reinforced Concrete Beams with and without FRP Web Reinforcement under Pure Torsion," Journal of Bridge Engineering, vol. 21, no. 3, article no. 04015070, 2016.

L. F. A. Bernardo, B. M. V. C. Filho, and B. Horowitz, "Efficient Softened Truss Model for Prestressed Steel Fiber Concrete Membrane Elements," Journal of Building Engineering, vol. 40, article no. 102363, 2021.