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)

Table 11.4-4 Moment distribution
Braced frame analysis 417
A B c
l:cols AB BA l:cols BC CB
DF(%) 84 16 15 79 6
FEM(kNm) 0 -651 +651 0 -300 +300
Balance +547 +104 -53 -277 -21
co -26 +52 -10
Balance +22 +4 -8 -41 -3
co -4 +2 -2
Balance +3 +1 -2
l:(kNm) +572 -572 +644 -320 -324 +288
At B: BA: (~col): BC = 15%: 79%: 6%
Fixed end moments (FEM) (Table 11.4-4):
Span AB:
Span BC:
12\~ 82 = 651 kNm
36 ~2 102 = 300 kNm
Since the moments 572 and 644 kNm at the ends of the beam ABare of
comparable magnitude, the sagging moment at the centre of the beam is
very nearly the maximum and has a value of 368 kNm, i.e. (122 x 82/8) -
(572 + 644)/2. This is to be compared with the value of 730 kNm given in
Fig. 4.9-6: Case 3, which assumes zero moment at the support A.
An analysis using the complete storey sub-frame, as in Example
11.4-l(b) with the .full imposed loading on spans AB and CD, gives
values of 573, 642 and 318 kNm for the moments designated AB, BA
and BC respectively. This indicates the relative accuracy of this two-span
sub-frame.
Example 11.4-l(d)
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 subframe
of Fig. 11.4-1 (f).
SOLUTION
Since the span BC is greater than either of the two adjacent spans, the
solution for BC using the sub-frame in Fig. 11.4-1(f) can also be taken
to give the column design moments (BS 8110: Clause 3.2.1.2.3). This
sub-frame is obviously of much more use when the structure has more
spans than the one being here analysed. Since the analysis of the complete