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)

302 Reinforced concrete slabs and yield-line analysis
energy dissipation for the length I
= mn() AI cos a A + mnOsl cos as
= mn(}A[A + mn(}s/s
where /A and Is are respectively the projections of I on the axes of rotation
for the rigid regions A and B. That is,
where m 0
energy dissipation for length I of yield line
= m "' [projection ?f t] [rotation of rigid r_egionJ
n Li on an axts about that axts
is the normal moment per unit length on the yield line.
(8.4-1)
Example 8.4-1
A square slab with built-in edges is isotropically reinforced with top and
bottom steel (Fig. 8.4-2). Determine the intensity q of the uniformly
distributed load that will cause collapse of the slab.
SOLUTION
A reasonable pattern of positive and negative yield lines is that shown in
Fig. 8.4-2. Consider a unit virtual deflection at point e:
external work done by the loading = jqL 2
(where j unit is the average deflection of the load). From eqn (8.4-1),
energy dissipation on the positive yield line ae
= mn [ (ae) cos 45° X L~ 2 + (ae) cos 45° X L~2 ]
= 2m since (ae) = ~/cos 45°
and from eqn (8.3-11),
mn = m
'am
I
------- a.m
lm
m
a
T
L
1
I· L
.,
Fig. 8.4-2