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)

304 Reinforced concrete slabs and yield-line analysis
Example 8.4-2
The simply supported rectangular slab in Fig. 8.4-3 is isotropically
reinforced with bottom steel, such that the yield moment of resistance
per unit width of slab is m for bending about any axis. Determine the
required value of m if the slab is to carry a uniformly distributed load of
intensity q.
SOLUTION
A reasonable yield-line pattern, defined by the parameter a, is shown in
Fig. 8.4-3. Consider unit virtual deflection along EF.
External work done by the load
= J qzdA (where z is the deflection of the elementary area dA)
= q x (volume swept by the slab as EF undergoes unit deflection)
= q [2 x jbal + !b(1- 2a)/J
qbl
end
pyramids
= 6 (3- 2a)
central
prism
(8.4-2)
From eqn (8.4-1),
energy dissipation for yield line AE
= m [b~~ + b~F]
energy dissipation for yield line EF
_ [ 2 x (1 - 2a)l]
- m b/2
Fig. 8.4-3