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)

Structural behaviour 233
CUrve II
(Unsymmetrical
longitudinal
relnforcement)
T
To
T 1
To
o 0·5
MIMo
(a) Behaviour
1·0
o~------~--------~
1
MIMo
(b) Design
Fig.6.10-1 Interaction oftorsion and bending [44]
For the particular case of (h = 1, their curve again resembles Hsu's curve
(1).
In current design practice, the reinforcements for torsion and bending
are calculated separately and then added together. The rationale for this
procedure is illustrated in Fig. 6.1O-1(b) [44]. In the figure, the ordinate
TI Tu = 1 on the vertical axis represents the strength in pure torsion of the
member with torsional reinforcement only; the abscissa MI Mu = 1 on the
horizontal axis represents the strength in pure bending of the same
member with flexural reinforcement only. Point C represents the design
procedure of adding torsional and flexural reinforcements. As Hsu and
Kemp [44] have pointed out, the addition of the torsional and flexural
reinforcements increases both the pure torsion and the pure bending
strengths, as illustrated by points A and B.
The interaction oftorsion and shear is not quite understood [33-35]. For
beams without links, a circular interaction curve has been suggested
[44, 45]:
(iuY + (~Y = 1 (6.10-2)
where T and V are the torsion and shear combination that can be resisted,
Tu is the strength in pure torsion and Vu that in shear (and the accompanying
bending). Insufficient test data are available for beams with links. In
British design practice, as explained in Section 6.10(a), the reinforcements
are calculated separately for torsion and for shear and are then added
together.
The behaviour of members in combined torsion, bending aud shear is
even less understood [33-35]. For design purposes, it would seem to be
conservative to calculate reinforcement requirements separately and then
add them together [43, 47]; as Goode [38] has pointed out, the loading
arrangement which gives the maximum torsional moment may not
simultaneously give the maximum bending and shear.