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)

414 Practical design and detailing
accuracy when applied to relevant continuous beams. This example does
show, however, the main danger in the use of such coefficients in that they
give no indication even of the possibility of a hogging moment at the centre
of this three-span continuous beam (which was clearly shown in Fig.
4.9-7(b) ). This possibility should always be considered when such
coefficients are used.
This continuous beam sub-frame (Fig. 11.4-1(g)) is an idealization
which ignores any end fixity that may be imparted by the columns. If this
sub-frame is used in a rigid frame analysis, as here, it is obviously prudent
to provide some reinforcement in the top of the beam at the ends A and D
even though the sub-frame analysis does not indicate any such need. In
Example 11.4-1(b) that follows, it will be seen that the value at the end
(110 kNm) is some 57% of the initial fixed end moment (192 kNm). This
is because of the high stiffnesses of the columns relative to that of the
beam, and the normal figure may well be somewhat less. Hence, a value of
some 30-40% of the initial fixed end moment may be more appropriate for
use in design.
Example 11.4-l(b)
With reference to the braced frame in Example 11.4-1(a) and Fig. 11.4-3,
calculate the maximum sagging moment in the span BC; use the sub-frame
of Fig. 11.4-1 (b). Compare the moment so calculated with that shown in
Fig. 4.9-6: Case 2.
SOLUTION
For clarity, Fig. 11.4-1(b) is redrawn as Fig. 11.4-4, which also shows the
relevant dimensions and loadings.
For the dead and imposed loading as above, and using the method of
moment distribution with relative EI values as given in Fig. 11.4-3:
Distribution factors (DF) (Table 11.4-3):
At A, D:
At B, C:
LCO!S (2 X 2/3) 0.667/0.792 84%
AB (2/8) 0.125/0.792 16%
BA: (Lcols): BC = 2/8: (2 - 2/3): 2/10
= 14%: 75%: 11%
36kN/m
A B
1-
Bm
·I-
122kN/m
36 kN/m
c D
10m Bm ..j
.T
+
3m
3m
j_
Fig.ll.4-4 Storey sub-frame