Grid Strut-Tie Model – Strength Analysis of Torsional Beam

The evaluation of the 3-D grid approach was carried out using the ultimate strength of 60 reinforced concrete beams subjected to pure torsion to failure by Hsu (1968), Rasmussen & Baker (1995), and Koutchoukali & Belarbi (2001). For purposes of comparison with current codes of practice, the ultimate strength of the beams was also evaluated using the AASHTO-LRFD (2014) and ACI 318-14 (2014) design provisions, Hsu & Mo (1983)’s method, and method of Rahal & Collins (1996).

Strength Analysis of Torsional Beam-01

The ultimate strength of each of the 51 torsional beams evaluated with the existing and proposed methods are compared in Table. It must be noted that all the methods overestimated the experimental capacities. On the other hand, the ultimate strengths were evaluated satisfactorily by the proposed 3-D grid strut-tie model approach. Thus, the proposed approach can be conservatively used for members under torsion.


  1. Hsu, T. T. C. (1968) Torsion of Structural Concrete, ACI Journal, Vol. 18, pp. 261-306.
  2. Rasmussen, L. J. and Baker, G. (1993) Torsion in Reinforced Normal and High-Strength Concrete Beams – Part 1: Experimental Test Series, ACI Structural Journal, Vol. 92, No. 1, pp. 56-62.
  3. Koutchoukali, N. and Belarbi, A. (2001) Torsion of High-strength Reinforced Concrete Beams and Minimum Reinforcement Requirement, ACI Structural Journal, Vol. 98, No. 4, pp. 462-469.
  4. American Concrete Institute (2014) Building Code Requirements for Structural Concrete (ACI 318M-14) and Commentary(ACI 318RM-14), Farmington Hills, Michigan, USA.
  5. American Association of State Highway and Transportation Officials (2014) AASHTO LRFD Bridge Design Specifications, 6th Edition, Washington D.C., USA.
  6. Hsu, T. T. C. and Mo, Y. L. (1983) Softening of Concrete in Torsional Members, Research Report No. ST-TH-001-83, Department of Civil Engineering, University of Houston, Texas, USA.
  7. Rahal, K. N. and Collins, M. P. (1995) Analysis of Sections Subjected to Combined Shear and Torsion – A Theoretical Model, ACI Structural Journal, Vol. 92, No. 4, pp. 459-469.

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