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)

Analysis of framed structure (BS 8110) 409
columns above and below. The ends of the columns may be assumed
to be fixed unless the assumption of a pinned end is clearly more
appropriate.
Thus, for the braced frame in Fig. 11.4-1(a), the sub-frame in
Fig. 11.4-1(b) may be used for the beams AB, BC, CD and for
the column moments at that level. According to BS 8110:
Clause 3.2.1.2.2, it is normally necessary to consider only two loading
arrangements for a braced frame (Fig. 11.4-1(a)) or its associated
sub-frames (Fig. 11.4-1(b)):
(1) All spans loaded with the maximum design ultimate load
(1.4Gk + 1.6Qk)· See Fig. 11.4-1(c).
(2) Alternate spans loaded with (1.4Gk + 1.6Qk) and all other
spans with the minimum design ultimate load l.OGk· Thus,
for the span moment in AB, the loading would be as shown in
Fig. 11.4-1(d). Similarly, for the span moment in BC, the
loading for that span would be (1.4Gk + 1.6Qk) while those for
AB and CD would be l.OGk·
(b) Sub-frames type II (BS 8110: Clause 3.2.1.2.3). The moments and
forces in each individual beam may be found by considering a subframe
consisting only of that beam, the columns attached to the ends
of that beam, and the beams on each side. The column and beam
ends remote from the beam under consideration may be assumed to
be fixed, unless the assumption of pinned ends is clearly more
reasonable. The stiffness of the beams on each side of the beam under
consideration should be taken as half their actual values if they
are taken as fixed at their outer ends. Thus, the Stlb-frame in
Fig. 11.4-1(e) would be used to analyse the oeam AB; similarly, that
in Fig. 11.4(f) would be used for the beam BC. The loading arrangements
for this type of sub-frames are the same as those exolained above
for sub-frames type I.
The moments in an individual column may be found from this type
of sub-frame, provided that the sub-frame has its central beam the
longer of the two spans framing into the column under consideration.
If, in Fig. 11.4-1, beam AB is longer than beam BC, then the subframe
in Fig. 11.4-l(e) should be used for the column at B (and also
for that at A, of course). On the other hand, if beam BC is longer
than AB, then the sub-frame in Fig. 11.4-l(f) should be used for the
column at B.
(c)
'Continuous beam' simplification (BS 8110: Clause 3.2.1.2.4.). As a
more conservative alternative to the sub-frames described above, the
moments and shear forces in the beams at one level may be obtained
by considering the beams as a continuous beam over supports
providing no restraint to rotation. Thus, the beams at the level
ABCD in the frame in Fig. 11.4-1(a) may be analysed as a continuous
beam on simple supports, as shown in Fig. 11.4-1(g). The
loading arrangements to be considered are the same as for the subframes
described above-see illustration in Figs 11.4-l(c) and (d).
Where the continuous beam simplication (Fig. 11.4-1(g)) is used,
the column moments may be calculated by simple moment distribu-