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)

314 Reinforced concrete slabs and yield-line analysis
(See Example 8.5-1 for proof that the projection of OA on them
moment axis is 1/df and that on the 0.75m moment axis is 1/dg.)
U(Region B) = m[ad]m[Os]m + 0.75m[ad]o.7sm[Os]o.7sm
Therefore
= m(de)(O) + 0.75m(ae)(Je)
= 0.75(ae)/(de)
U(A and B) [ de ae aeJ
= m df + 0.75 dg + 0.75 de
The lengths de, df, ae, dg, and de for the various a values may
conveniently be measured from a drawing drawn to scale. The reader
should verify that these are as recorded in Table 8.5-1.
Therefore
U(a = 25°) = m [~:~ + 0.75 x {i~ + 0.75 x ~:~] = 2.51m
Similarly
U = 2.39m(a = 30°)
2.55m(a = 40°) and 2.81m(a = 45°)
From the graph in Fig. 8.5-5(b),
U(minimum) = 2.38m
Since the external work is 8q sin 70° as in Example 8.5-2,
( · · ) 2.38m 0 317
q mtmmum = 8 sin 70o = . m
(b)
a(worst) = 32S by measurement
No, to obtain the absolute minimum collapse load, we need to
investigate all possible yield-line patterns and determine the worst
layout for each pattern. However, practical designers do not look for
such absolute minimum collapse load (see Part (c) below).
Table8.5-1 Lengths measured on a
drawing of scale 10 mm to 1 m
a de df ae dg
25° 2.5 4.5 5.4 12.0
30° 2.9 3.9 5.0 10.6
35° 3.2 3.4 4.6 9.2
400 3.6 2.9 4.3 7.9
45° 3.9 2.4 3.9 6.6