F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

232 Shear, bond and torsion
BS 8110: Part 2: Clause 2.4.6 states that for combined torsion and shear,
the torsion and shear reinforcements are calculated separately, and then
added together, in accordance with Table 6.10-1.
6.10(b) Structural behaviour
The interaction of torsion, bending and shear has been studied by Hsu
and others [44, 45]. For members in which the longitudinal reinforcement
is symmetrical about both the vertical and horizontal axes of the crosssection,
the interaction of torsion and bending is represented by curve (1) in
Fig. 6.1O-1(a), in which T and Mare the torsional and bending moment
combination that the beam is capable of' resisting, To is the ultimate
strength in pure torsion, and Mo that in pure bending. Curve (II) is the
interaction curve for members with asymmetrical longitudinal reinforcement;
for such members, the torsional capacity is increased by the
application of limited amounts of bending. More recently, Lampert
and Collins [43] have proposed the following interaction equations for
rectangular beams:
(T)2
M
l?1 T o + Mo = 1 (6.1O-1(a»
(~r -;.(ffo) = 1
(6.1O-1(b»
where el is the ratio of the yield force (Alfy) of the longitudinal steel at
the top (i.e. the ftexural compression zone) to the yield force (Asf y) of that
at the bottom; the other symbols have the same meanings as explained
earlier for Fig. 6.1O-1(a). Equation (6.1O-1(a» applies for yielding of
the bottom longitudinal steel and the links; eqn (6.10-1(b» applies for
yielding of the top longitudinal steel and the links. Lampert and ColIins's
interaction curve, therefore, consists of two parts, defined respectively by
eqns (6.1O-1(a), (b»; it is similar to Hsu's curve (II) in Fig. 6.1O-1(a)
except that there is now a kink at the intersection of eqns (6.1O-1(a), (b».
Table 6.10-1 Reinforcement for torsion and shear
(BS 8110 : Part 2 : Clause 2.4.6)
Vt > Vtmin
V> Ve
Nominal shear
reinforcement;
no torsion
reinforcement
Designed shear
reinforcement;
no torsion
reinforcement
Designed torsion
reinforcement only
Designed shear
and torsion
reinforcement