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)

324 Reinforced concrete slabs and yield-line analysis
(a) the design bending moment diagrams for typical strips;
(b) the design load diagrams for the edge beams.
Use lines of discontinuity as proposed by Wood and Armer.
SOLUTION
(a) The design moment diagrams for the x-strips are shown in Fig.
8.6-4(b) and those for they-strips in Fig. 8.6-4(c).
(b) The reactions required for the design of the supporting beams are
shown in Fig. 8.6-4(d) and (e).
Comments
(a)
Figure 8.6-4(b) shows that there is no load and hence no moments on
the x-strip 1-1. These strips must, however, be reinforced to the
minimum level required by BS 8110 (see Section 8.8).
(b) The slab in Example 8.6-1 is simply supported. If it had been
continuous over the supports, then the moment diagrams in Fig.
8.6-4(b) and (c) are still acceptable from the strength point of view,
but unacceptable from the serviceability point of view. Wood and
Armer have suggested that for such a continuous slab the designer
may assume that in each strip the points of contraflexure are located
from the supports at 0.2 times the span for that strip. Consider, for
example, the strip 6-6; the points of contraflexure would be assumed
at 0.2 x 5 = 1m from each end support, so that the bending moment
diagram for that strip becomes as shown in Fig. 8.6-1(c). The
moment diagram for each of the other strips is similarly obtained by
lifting the base line by the appropriate amount so that the positions of
zero moment coincide with the assumed points of contraflexure.
(c)
Wood and Armer's suggestions for stepped lines of discontinuity can
be applied to slabs with openings or slabs with different support
conditions, as illustrated in Fig. 8.6-5.
8. 7 Shear strength of slabs (BS 8110)
The shear strength of slabs is governed by the same general principles as
for beams (see Chapter 6). In design, the nominal design shear stress vis
calculated from eqn ( 6.4-1):
v
v = bd (8.7-1)
where V is the shear force due to ultimate loads, b the width of the slab
under consideration and d the effective depth. The design procedure for
slabs is essentially the same as that for beams (see Section 6.4), and only a
few comments are necessary:
(a) The design shear stress v from eqn (8.7-1) should not exceed
0.8Hcu or 5 N/mm 2 , whichever is less. Increase the slab thickness, if
necessary, to satisfy this requirement.
(b) If v is less than v c in Table 6.4-1, no shear reinforcement is required.
(c) If Vc :::s v :::S (vc + 0.4), provide minimum links in accordance with
eqn (6.4-2):