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)

294 Reinforced concrete slabs and yield-line analysis
(a) The yield lines divide the slab into several regions, called rigid
regions, which are assumed to remain plane, so that all rotations take
place in the yield lines.
(b) Yield lines are straight and they end at a slab boundary.
(c)
A yield line between two rigid regions must pass through the
intersection of the axes of rotation of the two regions (Fig. 8.2-l(c):
the supports form the axes of rotation).
(d) An axis of rotation usually lies along a line of support and passes over
columns.
A yield-line pattern indicates how a slab collapses, just as a plastic-hinge
mechanism indicates how a framework collapses.
8.3 Johansen's stepped yield criterion
This is the yield criterion in common use. It is based on the assumptions
that all reinforcement crossing the yield line has yielded and that all
reinforcement stays in its original direction, i.e. there is no 'kinking' [4] of
the reinforcement bars in crossing the yield line.
Before describing the stepped yield criterion, we shall first explain
the moment-axis notation. Suppose a slab is reinforced with a band of
reinforcement such that the yield moment of resistance per unit width of
slab ism for bending about an axis perpendicular to the reinforcement; this
information may be represented in abbreviated form by a line drawn
normal to the direction of the reinforcement and labelled m. Thus, in Fig.
8.3-l(a) and (b), the m 1 moment axis indicates that the slab is reinforced
to give a resistance moment of m 1 per unit width for bending about that
axis; similarly the m 2 moment axis indicates a resistance moment of m 2 per
m1
(c)
(d)
Reinforcements Moment axes
fa)
Reinforcement
(b)
Moment axis
Fig. 8.3-l