Structural Concrete - Hassoun

530 Chapter 15 Design for Torsion
Figure 15.6
sections.
Combined shear and torsional stresses: (a) solid sections and (b) hollow
15.6.1 Skew Bending Theory
The skew bending concept was first presented by Lessig in 1959 [2] and was further developed by
Goode and Helmy [3], Collins et al. in 1968 [4], and Below et al. in 1975 [5]. The concept was
applied to reinforced concrete beams subjected to torsion and bending. Expressions for evaluating
the torsional capacity of rectangular sections were presented by Hsu in 1968 [6,7] and were
adopted by the ACI Code of 1971. Torsion theories for concrete members were discussed by Zia
[8]. Empirical design formulas were also presented by Victor et al. in 1976 [9].
The basic approach of the skew bending theory, as presented by Hsu, is that failure of a
rectangular section in torsion occurs by bending about an axis parallel to the wider face of the
section y and inclined at about 45 ∘ to the longitudinal axis of the beam (Fig. 15.7). Based on this
approach, the minimum torsional moment, T n , can be evaluated as follows:
( x 2 )
y
T n = f
3 r (15.8)
where f r is the modulus of rupture of concrete; f r is assumed to be 5 √ f ′ c in this case, as compared
to 7.5λ √ f ′ c adopted by the ACI Code for the computation of deflection in beams.