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)

318 Reinforced concrete slabs and yield-line analysis
rn
• rn \ rJf_\
.rrf
, a·~ A'
d
c~
fa)
(b)
Fig. 8.5-8 Fan mechanism
Therefore, the total energy dissipation for entire fan mechanism
= m + m' "(
LJ e d) = m + m' 2 nr
r
r
= 2n(m + m')
The work equation is therefore
~ qr 2 + Q = 21l(m + m')
Therefore, if the distributed load is absent,
Q = 21l(m + m')
and is independent of the radius of the fan. Conversely, if the point
load is absent,
~qr 2
= 2n(m + m')
(c)
or
6(m + m')
q = 2
r
which reduces as r increases. In other words, where a slab supports a
distributed load, a fan mechanism always extends to a slab boundary;
where a slab supports a point load only, the fan mechanism gives a
constant value for the collapse load which is independent of the
radius of the mechanism.
In all of the Examples in Sections 8.4 and 8.5 the work method has
been used, in which the solution is obtain~d by equating the external
work done by the applied loads to the internal energy dissipation. All
yield-line patterns which the designer is likely to encounter in practice