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)

208 Shear, bond and torsion
(d)
(e)
(f)
Tests [25] have shown that (1) links which intercept a diagonal crack
near the top are relatively ineffective and that (2) a link, in addition
to the one crossed by the diagonal crack and within a close distance to
it, further increases the shear strength of the beam. Therefore, it is
desirable in design to limit the maximum link spacing to, say, 75% of
that above:
sv.maivertical links) = O.75d (6.3-9)
Example 6.3-1 also shows that, for bent-up bars (or inclined links),
sv.maibent-up bars) = (cot a + cot P)d
It was explained earlier, in connection with eqn (6.3-6), that both a
and P should not be less than 45°, so that
sv.max(bent-up bars) = (cot 45 + cot 45)d
= 2d
Again, taking 75% of this value for design, we have
sv.max(bent-up bars) = 1.5d (6.3-10)
When (!v and Sv satisfy the requirements in (b) and (c) above, the
capacity of the web reinforcement may for design purposes be
estimated by the truss analogy. The truss analogy assumes that the
web steel can reach its yield stress before other failure modes occur,
e.g. web crushing or compression zone failure. Tests [1, 2] have
shown that such premature failures can be prevented by imposing a
ceiling on the nominal ultimate shear stress. Denoting this nominal
stress by Vu (to distinguish it from the Ve in eqn 6.3-7), the external
shear force V must not be allowed to exceed
(6.3-11)
no matter how much web steel is used.
For a beam with web reinforcement, therefore, the shear resistance
may be regarded as being made up of the sum of the concrete
resistance and the web steel resistance:
V = Ve + Vs
or dividing by bd,
(6.3-12)
where Ve may conservatively be obtained from test results for beams
without web reinforcement (e.g. Fig. 6.2-6). In fact the web steel
does not only carry shear force itself, but it also increases the shear
carrying capacity of the concrete.
The truss analogy does not differentiate between links and bent-up
bars. When they are used in combination, the analogy gives their
shear capacity as the sum of their capacities when used separately.
The effects of links and bent-up bars used in combination are actually
more than additive [1]. Bent-up bars are more effective tban links in