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)

Yield-line analysis 293
8.2 Yield-line analysis
The yield-line theory pioneered by Johansen [2, 3] is an ultimate-load
theory for slab design and is based on assumed collapse mechanisms
and plastic properties of under-reinforced slabs. The assumed collapse
mechanism is defined by a pattern of yield lines, along. which the
reinforcement has yielded and the location of which depends on the
loading and boundary conditions. For the yield-line theory to be valid,
shear failures, bond failures and primary compression failures in flexure
must all be prevented. The moment/curvature relationship must resemble
that of Fig. 4. 9-1, having a long horizontal portion when the yield capacity
of the slab is reached; in practice, this restriction presents no difficulties
because slabs are usually very much under-reinforced.
Figure 8.2-1 shows some tyRical yield-line patterns for slabs in the
collapse state under uniformly dtstributed loads. A full line represents a
positive yield line caused by a sagging yield moment, so that the concrete
cracks in tension on the bottom face of the slab; a broken line represents
a negative yield line caused by a hogging yield moment so that tensile
cracking occurs on the top face. The convention for support conditions is as
follows: single hatching represents a simply supported edge, double
hatching represents a built-in edge, while a line by itself represents a free
edge. The following comments [3] should be noted:
Yield
lines
(a)
Simple support
(b)
Fig. 8.2-1
Simple support
(c)