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)

306 Reinforced concrete slabs and yield-line analysis
bending about any axis. The slab is simply supported along three edges
and fully fixed along the fourth edge. By considering a reasonable yieldline
pattern, such as the one shown in Fig. 8.4-4, determine the intensity q
of the uniformly distributed load that will cause collapse.
SOLUTION
The yield-line pattern in Fig. 8.4-4 is defined by the parameters x and y.
Consider a unit virtual deflection along EF.
External work done by the load (see eqn 8.4-2 of Example 8.4-2)
= q x volume swept
= q[ (2)(j)(5x) + (1) (5)(10 - 2x)]
= (25 - 1.667x)q
From eqn (8.4-1),
energy dissipation for yield lines AE and BF
=2m(~+ i)
energy dissipation for yield lines DE and CF
= 2m(-x-+~)
5- y X
energy dissipation for yield line EF
= m(lO - 2x + 10 - 2x)
y 5- y
energy dissipation for negative yield line AB
=m(~o)
Total energy dissipation
=10m-+-+--
( 1 2 1 )
x y 5-y
c
Fig. 8.4-4