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 shear reinforcement 207
Again, test observations have led to the following recommendations on the
use of eqn (6.3-6):
(a) the angle a should not be less than 45°;
(b) the spacing Sv should not exceed 1.5d; otherwise the angle P tends to
be less than 45°, with the consequence that the bent-up bar system
becomes ineffective; .
(c) the shear force carried by the bent-up bars should not exceed 50% of
the shear force V s carried by the web steel. (That is, at least 50% of
V s should be provided by links.)
It should be noted once again that the truss analogy is no more than a
design tool; though conceptually convenient, it presents an over-simplified
model of the reinforced concrete beam in shear [1, 2]. For example, the
truss analogy model completely ignores the favourable interaction between
the web reinforcement and the aggregate-interlock capacity and the dowel
force capacity; to this extent it tends to give conservative results, though
the conservatism reduces as the amount of web steel increases. The truss
analogy also assumes that the failure of the beam is initiated by the yielding
or excessive deformation of the web reinforcement, but in very thin
webbed reinforced or prestressed concrete beams (e.g. T-beams), failure
may in fact be initiated by web crushing; in such a case the truss analogy
would give unsafe results.
The above account of shear behaviour, together with that in Section 6.2
for beams without web reinforcement, may be amplified by the following
summary statements:
(a)
For a beam without web reinforcement, Fig. 6.2-6 shows that, given
the concrete strength leu and the longitudinal steel ratio e, a safe
lower bound value can be assigned to the nominal shear stress at
collapse. Designating this nominal shear stress as Ve (where the suffix
c will serve to remind us that we are referring to a beam without web
steel), a safe estimate of the ultimate shear strength would be
(6.3-7)
(b) Where web reinforcement is used, it remains practically unstressed
until diagonal cracking occurs, at which instant those web bars
that intercept the diagonal crack will receive a sudden increase in
stress [1]. If the amount of web steel is too small, the sudden stress
increase may cause the instant yielding of the web bars. The authors
[1] have drawn attention to the test observation that the web-steel
ratio ev (= Asv/ bSv ) should be such that the product ev!yv is not less
than about 0.38 N/mm 2 • For design purposes, we can round up 0.38
to 0.4, so that
ev/yv (minimum) ;;::: 0.4 N/mm 2 (6.3-8)
(c)
Web reinforcement may confidently be assumed to be effective, only
if every potential diagonal crack is intercepted by at least one web
bar. Example 6.3-1 shows that, for this to be possible, the spacing of
vertical links must not exceed
Sv ,mai vertical links) = d