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)

Effects of tors ion reinforcement 229
Diagonal
(concrete between
cracks)
Fig. 6.9-1 Lampert and Collins's space truss analogy [43J
T = ultimate torsional moment of resistance;
As = total area of longitudinal reinforcement;
Asy = area of the two legs of each link;
fy = yield strength of the longitudinal reinforcement;
fyy = yield strength of the links;
Sy = longitudinal spacing of the links;
x. = the smaller dimension between the corner bars, as labelled
in Fig. 6.9-1;
Y. = the larger dimension between the corner bars, as labelled in
Fig. 6.9-1.
Considering a length Sy of the beam. the (steel volume) x (yield
strength) products are respectively As fy Sy and A sy fyy(x. + y.). It is
desirable that the longitudinal bars and the links should yield simultaneously;
to achieve this condition, the volume-strength products should
be made equal [43. 44], i.e.
(6.9-1)
Lampert and Coli ins have found that, if eqn (6.9-1) is satisfied, then the
diagonal cracks (Fig. 6.9-1) can be assumed to be inclined at 45° to the
axis of the member. We recall that in Section 6.3, the truss analogy was
used to calculate the shear resistance of a beam. We shall now show that
the ultimate torsional resistance may be calculated, in a similar way, from
Lampert and Collins' space truss analogy.
With reference to Fig. 6.9-1, consider the intersection of the horizontal
legs of the links by the diagonal cracks. Since each crack can be assumed
to be inclined at 45° to the member axis, then on each horizontal face of
the member,
[ numer of horizontal legs]
intersected by a crack
Yt =- (6.9-2)