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)

Hillerborg's strip method 321
indicate that the designer, using his intuition, has decided to carry all the
load in the areas 1 by x-strips (i.e. strips spanning in the x-direction) and to
carry all the load in the areas 2 by y-strips. Suppose the uniformly
distributed load on the slab is of intensity q. Then a y-strip, such as A-A,
will be loaded along its entire length, as shown in Fig. 8.6-2, so that the
bending moment diagram is of parabolic shape with a maximum ordinate
of qb 2 /8. They-strip B-B will be loaded only for a lengthy at each end and
unloaded at the centre, because in the central length (b - 2y) the load is
carried by x-strips. Similarly, the x-strip C-C is loaded as shown. Thus,
once the decision is made regarding the lines of discontinuity, the designer
immediately has (a) all the bending moment values with which to calculate
the required reinforcement and (b) the support reactions required for
designing the supporting beams. But this is where design judgement
comes in. Referring to Fig. 8.6-2, the angle a defining the line of discontinuity
between areas 1 and 2 is up to the designer to decide. If, for
example, a is made equal to 90°, then the result is a slab reinforced for oneway
bending. By the lower-bound theorem, it is safe; but it is not
serviceable, because excessive cracking will occur near the edges in the
y-direction. Hillerborg has suggested that for such a simply supported slab,
the angle a should be 45°.
In Fig. 8.6-2, the bending moment diagrams for typical strips are as
shown. It is obviously impracticable to reinforce a slab to match these
moments exactly. Hillerborg chose to reinforce the full length of each
strip to withstand the maximum moment acting on it. However, even these
maxima themselves vary with the position of the strip. For example, the
maximum moment for a y-strip A-A is qb 2 /8 while that for B-B is qy 2 /2.
Hillerborg decided to have strips of uniform reinforcement giving a slab
yield moment equal to the average of the maximum moments found in that
strip. Thus the slab in Fig. 8.6-3(a) might be divided into three x-strips
of widths bt. b2 and b1 respectively, and three y-strips of widths ft. 1 2 and 1 1
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