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JOURNAL OF MATERIALS & CONSTRUCTION

ISSN: 2734-9438

Website: www.jomc.vn

Modified space-truss model for predicting the torsional capacity of ultra-high-performance concrete beams

Nguyen Vu Luat , Nguyen Vinh Sang

Abstract

Ultra-high-performance concrete (UHPC) beams exhibit enhanced post-cracking stress transfer due to fiber bridging, a mechanism not adequately represented in conventional torsion design provisions. This study develops a modified space-truss model (MSTM) to predict the ultimate torsional capacity of UHPC beams under pure torsion. The proposed formulation retains the three-dimensional space-truss analogy and thin-walled tube idealization, while explicitly incorporating the tensile contribution of UHPC through equivalent longitudinal and transverse tensile components. In addition, the inclination angle of the concrete strut is refined using equilibrium and strain-compatibility considerations rather than fixed code-recommended values. The reliability of the MSTM is validated using a compiled database of 40 UHPC beams from previous experimental studies and benchmarked against the truss-based provisions in ACI 318-19 and GB 50010. The results indicate that both code-based approaches tend to provide conservative predictions. In contrast, the proposed MSTM achieves improved agreement with experiments (mean value = 0.90 for  Tu,cal/Tu,exp) while remaining slightly conservative for design.

References

  1. Cao, X., Ren, Y.-C., Zhang, L., Jin, L.-Z., & Qian, K. (2022). Flexural behavior of ultra-high-performance concrete beams with various types of rebar. Composite Structures. 292: 115674. doi:https://doi.org/10.1016/j.compstruct.2022.115674
  2. Wang, Q., Song, H.-L., Lu, C.-L., & Jin, L.-Z. (2020). Shear performance of reinforced ultra-high performance concrete rectangular section beams. Structures. 27: 1184-1194. doi:https://doi.org/10.1016/j.istruc.2020.07.036
  3. Cao, X. et al. (2023). Torsional capacity of ultra-high-performance concrete beams using rectangle stirrup. Journal of Building Engineering. 69: 106231. doi:https://doi.org/10.1016/j.jobe.2023.106231
  4. Hsu, T. T. C. (1968). Torsion of Structural Concrete-Behavior of Reinforced Concrete Rectangular Members. American Concrete Institute. 18: 261-306. doi:10.14359/17572
  5. S.M.R. Lopes, L. F. A. B. (2009). Twist behavior of high-strength concrete hollow beams-formation of plastic hinges along the length. Engineering Structures. 31(1): 134-149. doi:https://doi.org/10.1016/j.engstruct.2008.08.003
  6. Rahal, K. N. (2013). Torsional strength of normal and high strength reinforced concrete beams. Engineering Structures. 56: 2206-2216. doi:https://doi.org/10.1016/j.engstruct.2013.09.005
  7. Rao, T. D. G., & Seshu, D. R. (2003). Torsion of steel fiber reinforced concrete members. Cement and Concrete Research. 33(11): 1783-1788. doi:https://doi.org/10.1016/S0008-8846(03)00174-1
  8. Fuad Okay, S. E. (2012). Torsional behavior of steel fiber reinforced concrete beams. Construction and Building Materials. 28(1): 269-275. doi:https://doi.org/10.1016/j.conbuildmat.2011.08.062
  9. Karimipour, A., de Brito, J., Ghalehnovi, M., & Gencel, O. (2022). Torsional behaviour of rectangular high-performance fibre-reinforced concrete beams. Structures. 35: 511-519. doi:https://doi.org/10.1016/j.istruc.2021.11.037
  10. Zhu, Y., Zhang, Y., Hussein, H. H., & Chen, G. (2020). Flexural strengthening of reinforced concrete beams or slabs using ultra-high performance concrete (UHPC): A state of the art review. Engineering Structures. 205: 110035. doi:https://doi.org/10.1016/j.engstruct.2019.110035
  11. Xue, J., Briseghella, B., Huang, F., Nuti, C., Tabatabai, H., & Chen, B. (2020). Review of ultra-high performance concrete and its application in bridge engineering. Construction and Building Materials. 260: 119844. doi:https://doi.org/10.1016/j.conbuildmat.2020.119844
  12. Yang, I.-H., Joh, C., Lee, J. W., & Kim, B.-S. (2013). Torsional behavior of ultra-high performance concrete squared beams. Engineering Structures. 56: 372-383. doi:https://doi.org/10.1016/j.engstruct.2013.05.027
  13. Ibrahim, M. S., Gebreyouhannes, E., Muhdin, A., & Gebre, A. (2020). Effect of concrete cover on the pure torsional behavior of reinforced concrete beams. Engineering Structures. 216: 110790. doi:https://doi.org/10.1016/j.engstruct.2020.110790
  14. Mohammed, T. J., Abu Bakar, B. H., & Muhamad Bunnori, N. (2016). Torsional improvement of reinforced concrete beams using ultra high-performance fiber reinforced concrete (UHPFC) jackets – Experimental study. Construction and Building Materials. 106: 533-542. doi:https://doi.org/10.1016/j.conbuildmat.2015.12.160
  15. Zhou, J., Li, C., Feng, Z., & Yoo, D.-Y. (2022). Experimental investigation on torsional behaviors of ultra-high-performance fiber-reinforced concrete hollow beams. Cement and Concrete Composites. 129: 104504. doi:https://doi.org/10.1016/j.cemconcomp.2022.104504
  16. Zhou, C., Wang, J., Jia, W., & Fang, Z. (2022). Torsional behavior of ultra-high performance concrete (UHPC) rectangular beams without steel reinforcement: Experimental investigation and theoretical analysis. Composite Structures. 299: 116022. doi:https://doi.org/10.1016/j.compstruct.2022.116022
  17. Ekkehard Fehling, M. I. (2012). Experimental Investigations on UHPC Structural Elements Subject to Pure Torsion. Conference: Ultra-High Performance Concrete and Nanotechnology in ConstructionAt: Kassel, Germany.
  18. ACI-318-19. (2019). Building code requirements for structural concrete and commentary American Concrete Institute, Farmington Hills, MI.
  19. 50010-2010, G. (2015). Code for design of concrete structures. China Architecture & Building Press: Beijing.
  20. Li, C., Zhou, J., Ke, L., Yu, S., & Li, H. (2022). Failure mechanisms and loading capacity prediction for rectangular UHPC beams under pure torsion. Engineering Structures. 264: 114426. doi:https://doi.org/10.1016/j.engstruct.2022.114426
  21. Imjong Kwahk, C. J., Jung Woo Lee. (2015). Torsional behavior design of UHPC box beams based on thin-walled tube theory. Engineering and Technology Journal. 7(3): 101-114. doi:http://dx.doi.org/10.4236/eng.2015.73009
  22. Fib. (2010). fib Model Code for Concrete Structures 2010.
  23. EN-1992-1-1:2004. (2004). Design of Concrete Structures, Reinforced Concrete Standards; Reinforced Concrete Construction Standards. European Committee for Standardization.
  24. Rausch, E. (1929). Berechnung des Eisenbetons gegen Verdrehung (Design of reinforced concrete in torsion). Berlin.
  25. Lampert, P., Thurlimann, B. (1971). Torsion und Biegung von Stahlbetonbalken (Torsion and Bending of Reinforced Concrete Beams). Bericht Nr 6506-2. Institut fur Baustatik, ETH Zurich: 101.
  26. CEB-FIP-90. (1990). Comite Euro-International du Beton. CEB-FIP model code 1990.Thomas Telford, London.
  27. CAN3-A23.3-04. (2004). Design of concrete structure for buildings.Canadian Standards Association, Mississanga, Canada.
  28. Bredt, R. (1896). Kritische Bemerkungen zur drehungselastizitat. Z. Ver. Dtsch. Ing. 40(28): 785-790.
  29. Hsu, T. T., Mo, Y. L. (2010). Unified theory of concrete structures. Wiley, West Sussex, U.K.
  30. Oettel, V. (2022). Steel fiber reinforced RC beams in pure torsion—Load-bearing behavior and modified space truss model. Structural Concrete. 24(1): 1348–1363. doi: https://doi.org/10.1002/suco.202200031
  31. Mahshid Abdoli, D. M., Mohamadrza Eftekar, Alireza Saljoughian. (2024). Torsional strengthening of T-shaped RC members with FRP composites using EBROG method: Experimental investigation and analysis. Construction and Building Materials. 437: 136829. doi:https://doi.org/10.1016/j.conbuildmat.2024.136829
  32. Mahshid Abdoli, D. M., Mohammadreza Eftekhar. (2024). Aggregate interlock and effective strain of FRP-strengthened flanged RC members subjected to torsion: Experimental evaluation and analytical modeling. Construction and Building Materials. 437: 136865. doi:https://doi.org/10.1016/j.conbuildmat.2024.136865
  33. Nguyen Vinh Sang , N. A. D., Nguyen Ngoc Thang. (2025). Analytical model for the torsional capacity of reinforced concrete beams strengthened with externally bonded frp sheets. Journal of Materials and Construction. 15(2): 21-29. doi:https://doi.org/10.54772/jomc.02.2025.794
  34. Nguyen Vinh Sang , V. N. L., Le Thi Thanh Hieu, Vu Hoang Minh Khang. (2026). A modified strut and tie model for predicting the torsional strength of steel fiber-reinforced concrete beams. Journal of Materials and Construction. 16(2). doi:https://doi.org/10.54772/jomc.02.2026.1237
  35. Abdul-Hamid Zureick, B. R. E., Andrzej S. Nowak, Dennis R. Mertz, Thanasis C. Triantafillou. (2010). Recommended Guide Specification for the Design of Externally Bonded FRP Systems for Repair and Strengthening of Concrete Bridge Elements.Transportation Research Board.
  36. AASHTO-LRFD. (2014). Bridge Design Specifications.American Association of State Highway and Transportation Officials.
  37. Zhang, Z., Xie, T.-Y., & Zhao, X.-Y. (2025). Torsional behavior of ultra-high-performance fiber-reinforced concrete beams: Testing, modeling and design recommendation. Journal of Building Engineering. 112: 113885. doi:https://doi.org/10.1016/j.jobe.2025.113885